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Meditations On Baking, Part 1

These notes reflect a learning curve that began as a chef’s apprentice in 1979. By 2005 during a less glorious career phase I had reached a temporary stopping point, so I began a compilation of my Chef’s notes as a distraction. Originally intended as a gift for my first-born son which I hoped would put the baker's fire in him, it took initial form as a short and sweet how-to guide with an accompanying formula calculating tool, and a jar of sourdough
culture. I’ve been reading and studying baking, and adding notes ever since. The original very modest formula calculator has undergone fifteen updates, each one elaborating and refining the design, as well as functions and practical applications. I intend to post it in the near future, along with a quick start guide, plus a much more detailed guide for more advanced bakers.

By the time this project began, my son was 22. He had trained in my kitchens, wetting his feet at age nine, and growing up surrounded by talented cooks. His interest and skills developed year on year. He learned about cooking, and kitchens, and the people who inhabit kitchens just as I had done; from scratch. I was a graduate philosophy student, bike mechanic, and house painter, but in a professional kitchen, a know-nothing. I didn’t even know how to hold a chef’s knife when I talked a local chef into accepting me as apprentice. That was a long time ago. Since then, I’ve been mentor to dozens like me. I believe I’m qualified to do a few more. 

What has become of that little project is The Unabaker Speaks. Meditations upon a life spent in kitchens, gastronomical commentary, artisan baking adventures in a very hot climate, philosophical discussion, occasional dialogue, a bit of storytelling, and an argument for baking as a binding principle for well-being. The first few chapters that follow deal specifically with understanding baking as a process phenomenon, and baker’s ingredients by a discussion of their material properties. Though aimed at cooks and bakers with an adequate knowledge base and some experience, ardent home bakers might also find it interesting and useful, perhaps even entertaining. For novice bakers and cooks, I’ll soon return to writing the “all you really need to know right now” beginners start-up guide, but if read carefully, these notes make for a good, though technically detailed introduction. If they’ve some facility with chemistry, even novices will get it, and very likely, quicker than I did. 

Baking is a meditative activity on the one hand, and on the other, much akin to performing lab experiments. It fosters well-being, methodological precision, and intellectual development. The Unabaker believes that more people baking more, and baking smarter is better for the world. 

Philosophical, analytical, curious, often humorous, and because he's experienced, old and grey, occasionally he’s been confused with a know-it-all. He’s not. He has too much experience to know it all. If you happen to like this little epistle, feel encouraged by it, or even thoughtfully provoked by it, look for The Unabaker Speaks, or contact him directly. 


What is Baking?

A simple definition is: “one of a just a handful of cooking methods, baking is the application of dried heat to composite preparations that require the removal of excess moisture in order to create a stable, edible structure”. Usually this is done using some sort of enclosed insulated box or cavern with a heat source, but baking can also be done on any surface that can be heated, regardless if it’s an insulated box or not. Cooking on a heated stone is baking. A griddle, Comal, or Tawa to cook english muffins, tortillas, chapati, and flatbreads is baking. Making toast is baking. 

Defining such a complex thing by cataloging its rudimentary elements isn’t very illuminating though, nor do we gain much understanding of the processes involved. If you want to learn to bake, or bake better, the simple truth is, you need to know more. How much more? It's up to you. Baking is not simply about making tasty stuff by ridding things of excess moisture. It’s a complex process during which a variety of physicochemical and microbiological changes occur. It’s helpful to understand these. Because it’s so complex, you can study it as much as you want, but the more you do, the more it will seem you don't know enough. It's part of the charm of our craft. Consider then, the following excellent, though slightly technical description of the process. I lifted it from a journal written by a group of enlightened gurus.1 It’s a precise description, though perhaps an imprecise quote.

“During baking, heat is transferred mainly by convection from the heating media, and by radiation from oven walls to the product surface followed by conduction to the product center. During this process, as the temperature within rises, moisture diffuses outward to the product surface, starches begin to gelatinize, forming interior structure, gases and steam cause the product to expand, the interior to develop characteristic porosity depending upon the type of baked product, and the exterior forms a crust, browning gradually as baking time increases. Eventually, the interior temperature has risen enough to cause a stable distribution of heat and moisture transport throughout the product.”

This is as clear and concise as any I've ever read. Of course, being concise, it is not complete. Other things are going on. On a timeline during baking, and in sync with the processes above, as the interior temperature of the product gradually rises, enzymes act upon starches at lower temperatures (about 30ºC) breaking them into sugars, yeast dies (45-50ºC), enzymatic activity increases (at about 50-60ºC), then ceases simultaneously to the beginning of protein (gluten) interaction with starches (60-80ºC). Of course, the development of aromatic and flavor compounds accompany. All of these processes occur depending upon the rate of heat applied, amount of heat applied, oven humidity, and the period of time over which heat is applied.2  

What are the differences between heat energy transfer from radiation, convection, and conduction? Radiation and convection refer to the heat energy created within the oven environment. The oven’s heat source creates convection currents of thermal energy, always flowing from hotter to cooler regions.3 Radiant energy is transferred from the interior surfaces of the oven to its center. As an oven preheats, it doesn't do so everywhere inside all at once, it does so gradually. The duration required depends upon oven dimensions, the various properties of the materials used to fabricate it, and the amount of heat energy being applied. Eventually, when all regions of the oven are more or less the same, the oven is said to have heated up. 

When thinking of convection it’s useful to imagine flow. Convected energy flow pertinent to cooks and bakers occurs in ovens, and in pots of liquid. We know from the Second Law of Thermodynamics that energy movement is always directed from regions of greater heat toward cooler regions, and that the rate of movement can be increased mechanically. The pot of liquid and the heat in the oven exhibit similar flow, but increasing the rate of flow has different implications for each. Some ovens have a fan that increases the rate of flow. Increasing the rate of flow speeds up the process. This is why convection ovens bake more efficiently, allowing lower temperature settings to be used. Unlike ovens, pots typically just have cooks to stir them. When a cook stirs a pot what happens? Stirring will help to equalize the diffusion of heat more rapidly in the pot of course, but it also decreases the amount of overall heat energy. Why does stirring aid one, and hinder the other? Because ovens have doors, stirred pots do not. Putting a lid on the pot will increase thermal flow, and since it also increases pressure within the pot, it increases the thermal conductivity of the material within (about which, more to come later). Nevertheless, pots occasionally still need to be stirred. A good cook tinkers with his stew as the process moves forward, tasting, adjusting and stirring periodically. 

Bakers aren’t so fortunate to be able to adjust a product once in the oven. There’s no baker's equivalent to the leeway cooks have. For this reason, accuracy of formulation becomes very important. Baking is a lot like executing a lab experiment. We can’t take something out half-baked, reformulate it by adding a bit more of this or that, then stick it back in, and expect success.

In any case, when radiant and convected thermal energy are applied to cookie dough, conduction takes the baton. Conduction is the direct transfer of heat energy on a molecular level across a heat gradient. The baton passes molecule to molecule. “Heat gradient” means a range of temperatures throughout the medium, always hotter nearest the heat source, gradually less and less so toward the point farthest from the source. Conduction is an irreversible directional process, always going from hot to not so hot across the gradient in any material. In a preheated oven, whatever it is that we put in the oven is the cooler region, and it remains cooler than the oven, absorbing more and more heat energy until turning completely to ash. Conducted heat energy is what actually cooks your cookie dough. When the thermal energy has been distributed evenly throughout the material, it is said to have stabilized, that is, reached a point of thermal and moisture equilibrium. Radiant and convected heat energy in the oven has been transferred to the cookie dough, and then conducted throughout. Your cookie is ready.

The report proceeded to details. I paraphrase perhaps, but accurately so: 

“During baking, the temperature and moisture distribution within the porous structure of the product can be predicted, but in order to do so, knowledge of the product properties is needed. These include density, specific heat, thermal conductivity, thermal diffusivity, and moisture diffusivity.”

These five product properties interrelate. Simply put, the first three, density, specific heat, and thermal conductivity, refer to physical properties of all matter, and which affect how something bakes, and the other two, thermal and moisture diffusivity, are process phenomena, that is, things that happen during the baking process which are how it bakes. 

In the oven, thermal energy acts by radiation and convection, and then by conduction to create movement within the material being baked. What is it that moves? On the molecular level where this occurs, it's the individual molecules that start to agitate under the influence of the conducted heat. Conducted energy transfer occurs directly, molecule to molecule. The moisture content of the item being baked begins to move after being heated sufficiently, but it takes a lot of heat energy to motivate moisture. This is why baking is a gradual process. If instead of water, we had some other innocuous liquid with much better thermal properties, then baking would proceed more rapidly. Perhaps there’s some parallel universe where it exists. In this one, water is what we have. Baking is gradual.

Bakeshop products are not piles of discreet ingredients. They are composite mixtures of ingredients. Many of the ingredients used by bakers have water content. Since the moisture in a product is part of its mass, the movement of it during the baking process is often referred to as “mass transfer”. Mass transfer has implications regarding changes to product density during baking, and of course also for heat transfer because moisture carries thermal energy from hotter to cooler regions of the product. As moisture moves, it obviously means the warmer region it moves from now has less mass, and the cooler region it moves to has greater mass. Because water also undergoes phase change from liquid to steam, it means that the total mass of the product decreases because some of the steam escapes through the surface of the item. Mass is directly related to density. Given the same volume of a substance the one with less mass (weighs less) is less dense. Less dense is generally preferred by humans. Fortunately for them, baking fosters this.

Heat and moisture move through a substance gradually. Gradual movement through a medium is called diffusion. Thermal energy and moisture diffuse across the temperature gradient of the product. As it does, various interesting transformations take place along the way. Starches gelatinize to form structure, trapping a fraction of the moisture within. Water undergoes phase change, meaning it turns to steam, and together with CO2 created by any leavening agents used, helps to create expansion; volume increases. Porous interior structure forms as a result of both starch gelatinization and expansion. Crust forms on the exterior, and gradually browns. When the interior temperature has risen sufficiently, there’s a stable distribution of heat and moisture throughout. The baking process has reached its ideal conclusion. Any continued application of heat beyond this point reduces moisture content, which is not ideal for deliciousness, or textural delight. Humans enjoy both of these qualities quite a bit. Bakers go to work every day aiming to provide enjoyment.

Bake shop formulations whether cake, pie, bread or custard have their own set of unique values for each of these properties and processes. What follows is a short tutorial.

1 Modeling of Simultaneous Heat and Water Transport in the Baking Process,  S.S. Sablani, M. Marcotte, O.D. Baik and F. Castaigne, LWT - Food Science and Technology, Volume 31 (3) - April, 1998

2 The information in this paragraph, and some of the wording was found in a very useful website, Bread and the Technology of Bread Production, Noël Haegens,

3 That heat energy always moves from areas of greater concentration to areas of lower concentration is explained by the idea of Entropy, which can be stated in simplistic terms as “ordered systems tend toward disorder”. The Second Law of Thermodynamics states that entropy never decreases over time, and reaches its maximum state at a point of thermal equilibrium. That heat flows to colder bodies, and never the reverse is an empirical finding; axiomatic in thermodynamic theory. Baking is not a perfect example of this since Entropy applies to closed systems of which sort, baking is not.



What is density? Density is an intrinsic property of matter that expresses a relationship between the mass of a substance, and a volume measure of it. “Intrinsic" means that it's a feature of a substance by virtue of the chemical composition and molecular structure of the substance. It is part of what a thing is, and cannot be removed from the thing. Density of a substance doesn't depend upon how much of it we have. No matter how much we have, or what geometric configuration it takes, it has the same density. A bucket of water has the same density as a bag, beaker, or box of it because the chemical composition and molecular structure of water don’t change unless some force acts upon it. A change in temperature, or the amount of pressure being applied are such forces that can alter the density of any material. For this reason, charts of densities for common substances reference a range of temperatures, and a specific amount of pressure at which the stated density value is true. Temperature and pressure matter, but a beaker full, or enough to fill your momma’s handbag does not.

How is density calculated? Density is the ratio of a unit of mass of a substance to a unit volume of it. In other words if I have a thimble, or a coffee cup, or the boot space of my old MGB, either of these would be the unit of volume, and then whatever the unit of weight we prefer to use (typically gram units) would be its unit of mass. Calculating density is easy. The density of a substance is the weight of it required to fill whatever volume measuring tool is used, and expressed as a ratio of weight per unit of volume. The formula for calculating the density of water, or any other substance is quite straightforward. It can be derived by dividing a unit mass of a substance (weight), by a unit volume of it. Density = Mass ÷ Volume. 

For example it takes 1 gram of water to fill a cubic centimeter measuring tool. Density is always expressed as weight per unit of volume. Therefore, the density of water is one gram per cubic centimeter (1 gram/cc3), sometimes expressed as 1 kilogram per liter (1kg/l). If we wanted to compare the density of another substance to that of water, we would use the same measuring tool, and then just weigh how much of the other substance it takes to fill it. If it requires more than 1 gram to fill the cubic centimeter, then its density would be greater than 1, and if less is required, it's density would be a fraction of 1. For example, even though milk is mostly water, it also includes a fraction of fat and milk solids, both of which are less dense than water. Thus, milk is less dense than water. Milk is .610grams/cc3. Here are some other common bakeshop ingredients including coffee because it's so commonly applied to bakers. Coffee is .330gram/cc3; sugar is .880; most fats are .900 to .950; flour varies depending on what type of grain and how much of the whole grain remains after milling, but for wheat flour it's around .593. Salt is an example of a baker's ingredient with greater density than water. It's about 2.17grams/cc3

Differences in the molecular structure of substances make a difference. Is the object solid, liquid or gas? Has it any interior void space, like wood or styrofoam? Is the item granular, like flour or seeds? Is it a composite material with various types of stuff as part of its makeup, like metal alloys and people? Objects with void space (air pockets) are less dense than if some of the void space is eliminated by compaction. What if void space is added? All items expand during baking, meaning that void space has increased. Consequently, the density of a baked item decreases as baking proceeds because it has expanded in volume. The fact that the density of baked items falls during the process has direct implications for thermal conductivity, and for heat and moisture transfer. Heat and moisture transfer is fundamentally what the baking process is all about. 

We don't normally think of ourselves as airy (though our colleagues might), but human bodies have lots of empty space between organs, and they have lungs functionally equivalent to personal floatation devices, plus we have unavoidable quantities of intestinal airiness. Calculating the density of water is easy, but the density of composites such as baked items, and for such odd substances as The Unabaker isn't as clear, but we can figure it out. Unabaker's density is related to his length, girth, weight, ratio of fat, muscle and bone, lung capacity, void space between organs, and volume of intestinal air. Careful calculations would likely show that the density of the The Unabaker is about 1.03 gram per cubic centimeter, which means he is slightly more dense than water. It's not a big difference unless he's a bad swimmer (he is). He might sink or float depending upon the water type, salt (he’ll float), or freshwater (he will not), and if he is inhaling (floats), or exhaling (sinks). We know that things with density lower than water tend to float. By inhaling mightily he might lower his density to below 1, in which case he floats even in freshwater. Is it surprising that things like bowling balls float? Actually, only some do. Bowling balls are manufactured to a specific dimension no matter the weight of it, so it makes sense that lighter bowling balls must have more void space than heavier ones. As a result, just like people, some float, others do not.

For bakeshop purposes, mass can be more practically understood as weight. What unit of volume measure we choose for the calculation makes no difference. We can do what most folks do, and use a graduated beaker, or we might use a shoe, a goblet, a great big box, or the trunk (boot) space of my old MGB. It will obviously require different weights of the substance to fill each of these, but as the unit of measure changes, the weight required to fill it changes. It doesn't change the density of the substance. Density of the substance that’s loaded into my sports car’s trunk, or your shoe does not change.

Even though the weight of a substance is a more practical basis for calculating density, and bakers own scales, they almost never do such things. As bakers, we don’t need to know precise values for individual ingredient density. We need only a general understanding of how they compare, one to the other. For example, most people know that a cup of water weighs more than a cup of flour, but do you know if water weighs more than sugar, and if you know which one weighs more, does it always follow that the heavier one is more dense? Yes, it does. For powdered, or granulated items, does it matter how fine it’s been ground? Is all purpose flour more dense than whole wheat flour? Perhaps you know, but do you know why? What about rye flour? Does it matter if it’s dark rye or light rye? How about vegetable oil? Oil seems like it ought to be heavier than water because it’s more viscous. It seems heavier, but of course, it’s not. Defying common sense again, vinegar seems like it ought to be the same as water, but in fact, it's not. Water is more dense than oil, therefore oil floats on water. Vinegar is more dense than water. Will water float on vinegar? What about butter? Butter is very much like oil in some respects, I mean, they’re both forms of fat. Does this mean butter is less dense than water? Yes, it does.

Knowing some of the characteristics of basic materials can allow us to deduce characteristics of others. Fat is less dense than water. Knowing this we can expect that suet, lard, butter, margarine, schmaltz, and vegetable oil are less dense than water. Water is more dense than flour, and flour weighs more than an equivalent measure of bran. We know water is more dense than flour, but so are eggs, sugar, salt, and even some types of starch. Why do we care about the density of flour, oil, sugar, salt or water? Density has direct implications for other properties of bakeshop formulations, and for the baking process, as well as activities that precede it. Proper measurement of ingredients is an important one of those activities.

We noted that two things affect density of a material. Temperature is one of those. Water has a density of one gram per cubic centimeter (1g/cc3), but it’s valid only for water at 4ºC (about refrigerator temp). As water temperature rises, density falls. Because no one owns cubic centimeter spoons, density of water is also expressed as one gram per milli-liter (1g/ml), or one kilogram per liter (1kg/l). We only need to select the most convenient method of measuring volume. For example, we put milk into a beaker, but tug boats into water. For big stuff, or oddly configured objects, the volume of an item is more conveniently gauged by its displacement of water. Some items make sense to measure one way, and some make sense to measure another. All we have to do is be consistent, and report the density of the material accordingly; grams of cobweb per metric bowling shoe, per US Standard handbag, or per big old box; it does not matter. Since, shoes, handbags and big old boxes all vary, and none are particularly convenient to use, normally you’ll find density reported as grams/cc3, or kg/liter. I’m unsure if the density of cobweb is known, or if different cobweb have different densities, but I’ll bet there’s an Arachnologist who does.

In some parts of the world people likely wonder how to convert the density of water if using quaint things like teaspoons. How many cubic centimeters of water is required to fill a US standard teaspoon? It turns out to be a tad more than 4.9289 cubic centimeters per teaspoon, which means there’s about 4.9289 grams per teaspoonful of water, or about 236.587 grams per US Standard cup.1 If you know that table salt is about 288 grams per cup, you also know that salt is quite a bit more dense than water. Can you guess how much flour it takes to fill a cup? The correct answer is: it takes a different amount every time you fill it. That’s one of the problems with measuring flour by volume. Volume measurements always vary because some days are more humid than others. Flour absorbs humidity. Volume measurements also vary because flour can be compacted. It's granular, therefore has void spaces between.

How is density relevant to the actual baking process? Density directly affects the thermal properties of items during the baking process. Each type of product has a different thermal profile that we use to predict the baking process. Density affects that profile. A discussion of those properties comprise the subjects of upcoming sections. 

The density of an item being baked changes during the process as temperature is applied continuously over time. Products lose moisture when baked, and also expand. Losing moisture means it has lost weight, and expanding means it has greater volume. Doing either alters density. Doing both, alters it more. Baking causes a double whammy decrease, though it does so to the delight of consumers of bread. The density of a baked bread loaf is about 41-45% that of the unbaked bread dough. Density is an important relevant factor that affects most of the other properties (except specific heat) of an item being baked, and it's something that baker’s deliberately tinker with from formulation to finished product. Depending on the amount of water used, you’ve got bagel, baguette, or ciabatta; english muffin, pancake, or crêpe. 

Does this mean that density is not an intrinsic property? We said density doesn't change. That’s true unless there’s a temperature or pressure change. Density is an intrinsic property of matter, but it’s not a constant value. “Tall” is an intrinsic property of the concept skyscraper, but its degree of tallness changes if certain things occur. Instead of temperature and pressure that affect density, adding another floor can cause tallness to change. It is still the substance known as skyscraper, only its tallness has changed. Density is an echo of a material's structure and composition, but the echo can be faint or strong.  

Baking can be regarded as a controlled drying out process. Many common baking ingredients such as eggs, butter, milk, yogurt, and fruit have varying degrees of water content. Whole eggs are about 65% water. Egg whites and milk are similar, about 88% water, and butter is about 15%. Though necessary to make a proper cake, when it comes to the baking process, the total amount of water in the batter is considered to be excess. Baking gets rid of the excess. While most of the water remains trapped within the baked matrix (gelatinized starch and gluten network), some of it evaporates away as it changes to steam. How much depends upon whether or not it’s baked in a mold, and the geometric configuration of the item. A product that’s baked in a mold loses less by evaporation than one that's free-baked because it has less exposed surface area. A long narrow loaf such as baguette will have more evaporative loss than a boule because a baguette has more surface area exposed. More surface area exposed to heat means there’s more crust formation. Crust is very much drier stuff than the interior crumb of a bread loaf, and it's the moisture lost due to crust formation that accounts for most of the loss. What is it that bakers do? Bakers strive to create a balance of residual moisture by applying the right amount of heat for the right amount of time. 

How does temperature change affect the density of an object? Suppose I have a big old box of cobweb at 4ºC, with density of X kilograms per big old box, and I gradually increase the temperature of the cobweb over a specified timeline by 10º, 20º, 30º and 40º. The Arachnologist's chart of cobweb density will show a gradually decreasing value for density at each stage of temperature increase. The same thing happens for all materials including water, flour, butter, eggs, salt, and sugar, and for all composite formulations of these. Density of a material falls as temperatures rise, but the rate of decrease isn't proportional. The decrease is continuous, but not steady. It decreases in smaller increments at each stage of temperature increase. Why does it do so? Because as the baking process continues, there’s less moisture to lose, and there’s a limit to the amount of expansion that occurs.

Doesn't this make sense? During baking, the internal temperature of bread dough rises, but the loaf doesn't expand continuously at the same rate, nor does it lose water weight in linear fashion. It expands more, and loses water more at the onset of temperature rise, then less, and less, and less. As baking proceeds, and crust forms, it limits the amount of further moisture loss, but moisture of the crumb remains relatively constant, dropping only slightly over the duration. The geometric mass of the as yet uncooked dough shrinks, but its moisture is bound in the starch gel, and as all bread crafters know, expansion of the dough mass has limits. Most moisture is lost prior to crust formation, which happens before it browns, and most expansion will occur in the first 8-10 minutes of bake time. After being removed from the oven, more moisture is lost through the crust. This accounts for sometimes soggy crusts if baking was not carried out properly before hand, or if crust formation took place too early in the process.

One might observe that cake batter is not the same thing as cake, so it stands to reason that each has a distinct density. Cake will naturally be lighter than batter because it has gained volume during baking (has more air in it), and lost moisture. We can very easily calculate the density of a specific cake batter, and do the same for the cake made from it. Does that mean that these two things are distinct entities? We can also predict changes to density that take place as it is baking, and plot these changes on a graph. As a result, specialty thinkers about stuff that happens, called Phenomenologists, might argue that the two things are in fact the same thing, but appear to be distinct due to being in different phases. Water is water, but it can be ice, liquid, steam or condensate. Batter and cake are simply phases of the same thing. 

Another Phenomenologist interested also in the classic philosophical Problem of Identity (especially as it applies to the identity of baked entities) might offer a counter argument to disprove the identity of batter to cake. Such an argument might be something like the following. Suppose we showed photos of a slab of bacon, a crown roast of pork ribs, a picnic ham and a platter of nice sausages to a very smart pig. While it’s doubtful that we could get useful input one way or another by asking cake if it feels identity to batter, pigs have cognitive skills, and therefore we should take their assessment to heart. After all who knows “pigness" better than pigs? Would the pig recognize the photos of pork products, and identify these as being pig, or deny it completely? In much the same way philosophers discuss problems with the concept of “Identity”. What sorts of things prove that I’m the same fellow as I was long ago? Since I’m the only one that has continuous observation of myself, it's not testable data. No one can independently confirm my self-observations, and what about when I’m unconscious? I can't even provide confirmation! The evidence is unconvincing. Problems like these proliferate in Philosophy, and its practitioners actually do stuff like wonder if that little boy in the photo is the “same” as the old man in the mirror. 

How does the age old problem of Identity relate to baking? The study of batter growing up to be cake, if not altogether simpler, it’s at least possible to learn some useful and verifiable specifics. Instead of quibbling Phenomenologists, we have food scientists armed with mathematical models, and computers, and diffusion equations to demonstrate the identity of batter to cake, and they’re happy to show us how it’s so. The food scientist's argument for the identity of those two things is simple: the one cannot be without the other.2 They describe batter and cake identity as a process phenomenon. They know that batter, if subjected to heat, undergoes physico-chemical changes, and that density (among such) always changes gradually along a timeline in accordance with the gradual rise of internal temperature. They can describe the process, and also predict it. On the other hand, by looking at his baby photos, who could have predicted The Unabaker? 

Batter and cake do not really constitute two distinct things. It’s not a change of identity, it’s merely a linguistic convention to give different stages of the same process different names. The advantage scientists have over Phenomenologists is that the entities being tested can be regularly observed by any interested party, all manner of tests can be independently performed, and the behavior of batter when heated can be predicted. None of which is true of The Unabaker. Batter when subjected to heat becomes cake. Doing so involves numerous substantial changes. Changes to a product's density is one of the more noticeable ones. Bakers do not wrestle with problems of Batterness, Cakeness or Breadness. 

The baking process alters both the chemistry, and the molecular structure of things. During baking, cake batter gradually loses moisture, and expands in volume. The ratio between mass and volume has fundamentally changed in both critical respects. What is it that bakers do? They alter the density of baked items very deliberately, but most of the time while never thinking that’s what they’re about. Goopy batter, becomes a light sponge texture that can be sliced. Liquid eggs and cream become silken custard. A blob of dough turns into ultralight Ciabatta. It’s just as simple as that.

A good project for an aspiring food science graduate paper might be to create before and after charts for densities of typical bakeshop products, along with flow charts that detail the movement of moisture and heat. Imagine how pointless that would be as far as most baker's are concerned, yet there’s probably some practical application for this knowledge. Even if there's not, can it ever be said that there’s such a thing as excess knowledge? 3

1  Here’s another way to express the density of water: one gram = 1/29 fluid ounce, and a cubic centimeter = a little bit more than 1/3 inch in all 3 dimensions. The density of water = 1 gram per cubic centimeter, or using the conversions above, we can express water density as .0344827586206 fluid ounces per cubic approximately one-third of an inch. There are 4.9289 of these cubic thirds of inches of water per teaspoon. Is it any wonder that the metric system is favored? 

2  This might possibly open the door to curious Existentialist thinkers, but I hope not.

3  The Unabaker wonders, are there persons or institutions responsible for eliminating the excess, analogous to the baker ridding pie of some of its moisture, and if so, does eliminating excess knowledge makes us more or less dense?


Specific Heat

Every object has specific heat capacity. You, your kayak, and my bike have it. Flour, eggs, butter, milk, sugar, salt, flavorings, and water have it. Bakers use these basic ingredients to make complex composites. Composites such as pie dough, cake batter, cookies, and custard have it. 

What is Specific Heat? Specific Heat is another intrinsic property of matter. How does it relate to density? Specific heat of a material is not influenced whatsoever by the density of that material, but both density and specific heat are factors in determining a material's thermal properties. The specific heat capacity of a material is its ability to change temperature. What's it take to make something increase in temperature? It takes energy input, thermal energy. If it takes more energy to heat it up, it is said to have greater specific heat than if it takes less energy to heat it up. 

Specific heat is normally understood as the amount of thermal energy required to raise the temperature of one unit of mass of the substance by one unit of temperature. For example, let’s stipulate we want to apply enough heat to 100 grams of water, cookie, cupcake and cobweb to raise the temperature of each by 1ºC. How much heat it requires to do so would be the specific heat capacity of that material. Items with higher specific heat capacity require more energy to raise their temperature. We might then usefully compare one to the other to determine appropriate uses for each. I’m no Arachnologist, but my guess is cobweb requires less heat energy than water, and therefore has lower specific heat. Water is used abundantly by bakers, but I know of no bakeshop formula that requires cobweb, yet. Perhaps a molecular gastronomist  can create one. After all such folk like to do stuff like cook things in hay. How much different is cobweb from that?

We know from the First Law of Thermodynamics that any object will remain at rest, or if it’s in motion, will maintain its current rate of motion in a straight line unless a force acts upon it to either make it move, change direction, speed up, or slow down. This feature of things is called Inertia. Inertia is not so unlike when I’m on the couch, unresponsive to routine stimuli. As long as the stimuli is typical The Unabaker remains at rest. It’s an imprecise analogy of course, because Inertia, and the laws of thermodynamics apply to particles, atoms, and the collections of atoms that we call the elements Hydrogen, Oxygen, Potassium, Iron, and Carbon for example. The sort of inertia we’re talking about in baking is Thermal Inertia which is not the same as what the First Law talks about, but it’s analogous. A silly illustration follows.

Since I’m a complex collection of chemical elements, let’s imagine that laws of thermodynamics describe the behavior of The Unabaker on his couch. Something sufficiently interesting has occurred to make him sit up. This would be akin to the force necessary to change an object at rest into an object that moves. What happened to make Unabaker move? Perhaps his creditors have gathered angrily at his sidewalk, or the neighbors are at it again, or maybe there's a knock upon his door along with noises that sound like, “Open up, it's the FBI!”. Inertia informs us that unless some force acts upon an object, things go merrily along as usual. The Unabaker nods off, and his cookie dough remains at rest on the countertop until moldy. The specific heat capacity of cookie dough is something we can know. How much heat energy must be applied to cookie dough to make it become cookie is what’s called its specific heat capacity. The force required is always the application of thermal energy. The FBI is almost never involved. 

Here’s another silly, but practical example of why specific heat is a useful thing to know. Imagine it's a very cold day in the mountains, and The Unabaker desires to go skiing. He doesn't own a boot warmer, so he decides to warm them up in the oven. The Unabaker owns very expensive ski boots, made using high impact polycarbonate plastic, weighing 3 kilograms. What amount of thermal energy is required to warm them up by 20ºC? Unabaker wishes he had known the answer! Depending upon the exact formulation of polycarbonate from which his boots are fabricated, the answer will vary, but it’s possible to know it. Besides knowing the specific heat of boots, The Unabaker desires to know how much heat it takes to warm up tater tot, burrito, and pie. These things are possible to know as well, but to do so precisely requires all of that hoo-haw the lab folks use. Instead, bakers just rely upon known formulations, specific mixing and handling methodology, and tried-and-true time and temperature settings. Part of what food scientists do is test products to find out what is "tried and true”.

When we talk about how much heat it takes to raise the temperature of a substance by 1ºC, we express it as a caloric value. What is caloric value? Caloric value is a measure of an item’s energy. In fact, it’s a measure of heat energy. Food is assigned a caloric value so consumers of food can easily assess how much of it they require to maintain stasis, i.e. remain alive, while neither expanding nor contracting. Understanding living things in terms of how efficiently they utilize energy taken from their environment has implications for Science of course (the concept of entropy in particular), but also for such things as Ethics, and even Theological inquiry. For understanding such things as the specific heat of cookie, the caloric value of the cookie and its weight are essential variables of the calculation.1 

Everyone knows about calories because we all desire to find the correct amount of these required to keep us going. Since calories are just units of heat energy, our caloric intake is nothing more than the measure of additional heat energy that’s been applied to our systems. Another imprecise analogy to help visualize this occurs to Unabaker. If we desire to effect change to the substance called The Unabaker, then we can add more calories to it. Its increased girth is very akin to the temperature change effected by the addition of heat to burrito. The number of calories required to increase Unabaker girth by a specific degree is the specific heat capacity of The Unabaker. “Everything expands when subjected to heat” is an example of a true truism. We know that adding burrito, tater tot and pie to The Unabaker is adding heat energy to it. If we add more burrito than required, The Unabaker expands.

Why is specific heat important for bakers? It’s important because water has a very high specific heat capacity, meaning that it takes a lot of heat to raise the temperature of water. Water has a much higher specific heat capacity than any metal. This should be obvious since we know that an aluminum pot heats up rapidly, but when we put water into it, it takes quite a bit of time to heat the water. Why? Because water requires more energy to heat up than does aluminum. It has greater specific heat capacity than aluminum. Properties such as specific heat, density, and thermal conductivity (the next topic) are not only fundamentally related, but all are very much influenced by water content. 

What's the most obvious implication for the baking process? We should expect a very moist medium such as cake batter to have higher specific heat than bread, and custard even higher. Why so? Because, the more water content in a formulation, the higher will be it's specific heat. Of all the baker's ingredients, water has the highest specific heat capacity. Since water is a major component of many bake shop formulae, baking takes more time than if it was not. Baking is a gradual process because, just like Unabaker, inert on his couch, it takes a lot of heat energy, and a lot of time to motivate water. The movement of heat and water during the baking process are topics for the next two meditations.  

The math required to calculate Specific Heat capacity is more involved than for computing density, but it’s not so complex either. The formula is C= q÷(m△T). In plain english it reads, Specific Heat = the Amount of Heat Energy Added ÷ (Mass x its Change in Temperature). Knowing it is in no way necessary to bake cookies, or to warm up boots, but it’s how scientists do stuff like analyze formulae for tater tots, and frozen burrito in order to advise The Unabaker how long he must reheat these, and at what temperature, and how much of these he requires. Where would he be without Science?

1 The Chemistry of Cookies, Stephanie Warren, 
Warren creates a cookie formula, then calculates its caloric value based upon a specified portion size. A chocolate chip cookie made according to her formula, and weighing 60 grams, has 110 Calories which converts to 460,240 joules [see note below]. 
-After sampling the cookie temperature before and after baking, Warren derives a value for the change in temperature equal to 169.45ºC. Specific heat of any material is calculated as Specific Heat = the amount of heat added ÷ (mass x change in temperature). Known values can be inserted as follows: Specific Heat = 460,420 / (60x169.45). Solving the equation derives specific heat equal to 45.27 (joule per gramºC). 
-This result applies only to the cookie formula used, and would not be valid for any altered formula that changes the caloric value per 60 gram portion.

[In physics and chemistry, one "small calorie" (typically denoted by the lower case c abbreviation, cal) is the amount of heat required to raise the temperature of one gram of water by one degree centigrade. Joule (J) is the standard unit of energy used. It takes 4.184 Joules to do that, therefore one small calorie = 4.184 Joules. However, when talking about food calories, the definition of calorie is different. One food calorie is the amount of energy required to raise the temperature of 1 kilogram (1000 grams) of water by 1ºC. Food calories are an example of what's called a "large calorie" (using the upper case C abbreviation, Cal), also known as kilocalorie (kcal) because 1 large calorie equals 1000 small calories. Therefore, 1 Calorie (Cal, or kcal) equals 4184 Joules. In which case 110 Calories is equal to 460,240 Joules. This is the amount of added heat energy represented by the cookie in Warren's example.]


Thermal Conductivity

Thermal conductivity is yet another intrinsic property of matter. The thermal conductivity of a material refers to its ability to conduct heat energy. All matter in the universe has thermal conductivity, including people, but for such sentient substances, testing for thermal conductivity is not considered to be an optimal activity. For that reason, precautions are generally taken to avoid this by wearing oven mitts, or using potholders. Nevertheless, it's a frequent occurrence in kitchens that accidental testing occurs. For example, on such occasions when the substance known as The Unabaker has undergone such a test, it always reacts surprised, terminating the test before accurate results can be determined. Observers have nevertheless surmised that Unabaker thermal conductivity appears to be quite good. 

Thermal conductivity is a measure of a substance's capacity to transfer heat energy from the warm side of the material to the cold side in a given time unit. Specifically, a material’s thermal conductivity is the rate of heat transfer through a unit thickness of the material, per unit area of it, per unit of temperature difference. For example, given an equally thick, one-meter length of aluminum, and the same of copper, both of which have a temperature gradient of 25ºC (the difference between the warm end and the cold end), the rate of energy transfer can be calculated.1 We would discover having done so that copper has greater thermal conductivity than aluminum for a number of reasons which include the fact that it has greater density than aluminum, as well as, lower specific heat capacity. 

We normally think of aluminum as a fine conductor of heat energy, and in the grand scheme of things it is, but would it surprise you to know that of all metals, aluminum has by comparison a rather high specific heat capacity, and therefore it conducts heat rather poorly? If that's so, why do we use it so much for cooking utensils? We use it because it's cheap, there's lots of it, it's easy to work with, meaning it's easily fashioned into various finished products, and also because it's a metal solid. Even a poor thermally conductive metal is much better than almost all other substances.

We like to think of the useful features of various materials as if they are virtues, in which case, aluminum, despite its high specific heat capacity, is quite virtuous stuff. In addition to those already noted, it's also a very lightweight material. Humans appreciate this because they can easily lift aluminum pots of water, whereas an iron pot, despite the virtue of being more thermally conductive, is inconvenient, and a gold pot, although it has the virtue of quite superior thermal conductivity, is both inconvenient and expensive. Since we are busy doing other stuff than studying the thermal properties of substance, it might come as a surprise to learn that, among all substances, metals are not the very best thermal conductors. It certainly surprised me. Although very efficient, copper, for example, is only about one-fourth as efficient as diamond. Imagine making cook's pots and bread baking pans from it! If suddenly there was a diamond stew pot craze on the buying network, we would need more diamonds than this planet has, a diminished fondness for sparkly adornments, and aspiring chefs would require lots more start-up capital for their taco stands as well. Despite its extremely virtuous capacity to conduct heat energy, diamond is a morally bereft electrical conductor. So bad is it that it could well function as a very, very virtuous insulator. Imagine having diamond pots to cook your goose, and diamond gloves to wear when rigging the power supply for your new Tesla!

Substances in our universe exist in what are known as phase states; solids, liquids or gases.It’s not at all uncommon for a substance to exist in all three, though not simultaneously. Water is a very simple example. Among the various phase states of substances in this particular universe, solids have the greatest degree of thermal conductivity, liquids less so, and gaseous substances the least. If you have good imagination, or perhaps read carefully the second meditation, you might already suspect why this is so. Density plays a big part. Greater density means better thermal conductivity. Solids are most dense, gases least so. Why does density matter? Because conduction is a molecule to molecule phenomenon, if the molecular structure of a material is more tightly spaced, then it's so much easier to share the thermal love. Solids have the most densely populated molecular neighborhoods, liquids much less so, and gases are, by far and away, the least neighborly of all.

When you're hanging out with your scientist pals down at the pub, and conversation invariably turns to the various rates of material thermal conductivity, what sort of measurement are we talking? The measurement for the thermal conductivity of a material is always expressed using units of power, called watts, a unit of area, typically the meter, and a unit of thermal energy, typically degrees Kelvin. For example, the thermal conductivity of a material is expressed as the number of watts per meter squared, per degree kelvin, or W/m2/ºK. There are different though equivalent ways of expressing the same thing using other, but equivalent units of measure. You can find this stuff in tables. No one actually does thermal conductivity tests when they're building things like power plants, or Formula 1 engines. They just look it up. Other folks have almost always done the tests already, though perhaps not yet for ski boots. Unfortunately for food engineers, since there are so many bakery food products, with so many formulations for each, if we want to know about the properties of frozen burrito or pie, then each one, and each variety of each one must be tested. 

What's the difference between conduction and conductivity? Conduction is one of three methods of thermal energy transfer, the other two being radiation and convection. Conduction takes place on the molecular level, but it is not an intrinsic property of matter. Thermal conductivity, on the other hand, is an intrinsic property of matter due to the material's chemical composition and molecular construction. Conduction is what happens, conductivity is the rate of the happening.

In simple terms, the rate of transfer of thermal energy is the same as the amount of heat energy transferred. The concept of the “rate” of something happening always implies a time period. Miles per hour, revolutions per minute, suckers born per second. So it is for the rate of thermal conductivity. In addition to a time unit, the calculation for determining a material's rate of thermal conductivity must also account for the geometric configuration of the material. The cross sectional shape and area of the material matters. A material's rate of thermal conductivity varies according to the thickness of the material under consideration. When reference tables give the thermal conductivity for common materials, they always refer to a unit thickness of material. Another important aspect of thermal conductivity is the direction of energy movement across a specific temperature gradient, always and irreversibly moving from the warmer side of the material to the colder side.2 Considering that thermal conductivity necessarily relates to a material’s geometry, and that it changes according to the dimensions of the material, we can see how this fundamental property of matter has direct implications for baking. Baked products are geometrical entities. When it comes to the rate at which thermal energy moves within your cupcake, cookie or cake, the exact geometrical configuration of the thing matters. 

How does the geometric configuration of a substance affect its capacity to conduct thermal energy? If you have a one meter long aluminum rod the diameter of which is 1cm, and apply heat at one end of the rod, aluminum will transfer the thermal energy to the opposite (cold) end of the rod more readily (faster), than if the rod is 2cm thick. During baking, since the geometry of a product undergoes change, the rate of thermal conductivity changes. What changed? The item being baked always expands during the process. The rate of thermal conductivity of an item is a function of bake time. Over time, the rate decreases, but it does not do so immediately, nor in steady fashion. I shall attempt to explain this aspect in more detail, but later.

How is thermal conductivity different from the specific heat of a material? Specific heat just means how much energy is required to warm up a given mass of some material by a certain degree, whereas thermal conductivity involves the concept of energy transfer; the intrinsic capacity of a material to relay thermal energy on the molecular level, molecule to molecule. Thermal energy has the jitters. It moves. It moves from hotter regions to cooler ones. Thermal conductivity is a measure of a material's rate of heat energy transfer, but rate of transfer is different from the actual movement of energy which is a concept called thermal diffusivity. Diffusivity means ability to spread through the medium. These two properties are related however. A material's value for thermal conductivity certainly affects the rate of diffusion of thermal energy throughout the substance. Most bakers don’t actually think of baking this way, but in fact, the baking process is all about the movement, i.e. the diffusion of heat and moisture through the medium being baked. Having read about this here, you can now talk intelligently about baking as a heat and moisture transport proposition, just like the science folk down at the pub do. Tell your friends that the movement of moisture, under the influence of applied thermal energy, through more or less dense materials, that exhibit varying degrees of specific heat, depending upon ingredients used, is what the baking process is all about. If you casually add that baking is really just a controlled drying out process, they’ll probably buy you beer. Thermal conductivity is a property of all substances; the intrinsic capacity of a substance to transfer heat energy.

To further illuminate the difference between specific heat and thermal conductivity, I’ll use the boot warming illustration again. Suppose that The Unabaker, instead of just popping his expensive boots into his little oven, and checking progress at various time intervals (or in his case, forgetting to do so), had wanted to know how much energy would be required to warm his 3-kilogram plastic boots to a specific degree of comfort. He wanted to know precisely, so he could set his oven accordingly, and attend to other stuff like find where he had put his gloves. In this case, knowing the specific heat of high impact polycarbonate plastic would have sufficed. He could just look it up. To understand the thermal conductivity for ski boots however, is not as easy. It requires figuring out the area of the ski boots, and also the thickness of the polycarbonate material used, and then running some tests, and by that time of course the lifts have closed. You may have already concluded that he would never have done such a thing. One of the things Unabaker is famous for is his First Law of Cognitive Dynamics, sometimes referred to as the Law of Conservation of Thinking. Among trained thinkers, it’s often casually stated as: there’s a finite number of thoughts we get; use them carefully. In this case, Unabaker was in a hurry to go ski. Immediately interested only in foot comfort on a cold morning, and trusting to dumb luck and bad habit, he didn't even bother to look up the specific heat of boots. 

Some materials are inefficient thermal conductors, and others are efficient. What's that mean? For any material, the less energy transferred through the medium in a given time unit, the lower is its thermal conductivity. Having lower thermal conductivity is what we mean by being less efficient; it doesn't transfer thermal energy well. Despite being a different feature of matter than thermal conductivity, the specific heat of a material nevertheless relates to it. It takes much more energy to raise the temperature of water than it does for copper, thus it has greater specific heat than does copper. A material with higher specific heat is less thermally conductive, that is, it transfers fewer watts of energy, and being less thermally conductive, we say that it’s less efficient. On the other hand, if more watts of energy are transferred, the material is a more efficient thermal conductor. Copper has a much lower specific heat than does water, and so, it’s a much more efficient thermal conductor. Water is a crappy (less efficient) thermal conductor, and because it’s so, we now have further insight into why baking is a gradual process. In short, high specific heat capacity goes hand in hand with lower thermal conductivity, and we say such things are less efficient thermal conductors. Low specific heat capacity implies higher thermal conductivity, and more efficient conduction. Water has very high specific heat, very low thermal conductivity. It’s inefficient. Because it is inefficient in this regard is not to say that water lacks virtue.3 

We know that water is not a good thermal conductor compared to other materials. Nevertheless, among bakeshop materials water is much more efficient than flour, eggs, sugar, salt, oil, butter and baking powder, all of which have various rates of conductivity lower than water. One might imagine as I did that oil would be a better thermal conductor than water because it can absorb more heat, but it turns out The Unabaker was confusing it's ability to achieve a higher temperature with its ability to transfer it. Oil has poor thermal conductivity. For this reason it’s used as a coolant in many mechanical applications. In addition, proportions of fats used in bakeshop formulae are most often lower than proportions of water bearing ingredients used. In cases where fats are used in large amounts, such as pie dough, short dough, and cookie dough, it implies that the composite thermal conductivity of such preparations is lower than that for ones that use greater portions of water, such as bread dough, cake batter, custard, and pie filling.

What sorts of things affect a material's thermal conductivity? Do materials have the same rate of conductivity at any temperature under all conditions? No, they do not. Materials have different rates of thermal conductivity at different temperatures, or if under more or less pressure. Increase the pressure, and you increase thermal conductivity.4 Isn’t this why pressure cookers cook your beans faster? In this respect, thermal conductivity is like density; temperature and pressure are two forces that can alter a material’s thermal conductivity. The values for thermal conductivity of materials can be found in tables that always reference a range of temperatures at a specific pressure. Change the temperature or the amount of pressure applied, and the material's rate of thermal conductivity changes. Do you see the connection with material density? If a material’s density decreases, thermal conductivity is slightly less. If it has greater density, it will have greater thermal conductivity. During the baking process, items become less dense because they expand (geometry changes) and lose moisture, which is to say, they lose weight. Baked items become larger and lighter during the process. Larger and lighter necessarily means less dense, and less dense means less thermally conductive.

At what temperature are materials more conductive, and when are they less conductive? It depends upon the material. Metal solids are generally more efficient thermal conductors at lower temperatures. Non-metal solids such as wood behave differently from metal solids. Liquids become less thermally conductive as temperatures rise, except for water. Water is an exceptional material! Water displays increased thermal conductivity as it heats up. Gaseous substances also have increased thermal conductivity when heated, but these are the least efficient thermal conductors, so the rise in conductivity when heated doesn't make them significantly more efficient. Baked products are not metal or wood, nor are they water balloons. Baked products are composite formulations of a bunch of different ingredients, each of which possesses its own intrinsic value for thermal conductivity. Therefore, the composite thermal conductivity for a bakery product after mixing (but prior to baking) should represent some balance of all. The baking process does interesting things to these composites however. For baked products there are three important considerations that affect thermal conductivity: temperature, moisture content, and density. Water, and water bearing ingredients such as egg, yogurt, cream, milk, and butter are important ingredients in the bake shop. Water is less efficient at conducting thermal energy at low temperatures. It is least efficient at just above the freezing point, but it becomes increasingly more efficient as its temperature rises to just below the boiling point. After reaching the boiling point, it undergoes what's called phase change, it changes from liquid to gas. Steam is gas. At this point, thermal conductivity of water is an entirely different story, but it’s one which I'm happy to tell.

Let’s visualize this. A pan of cake batter undergoes continuous temperature change during baking, as the internal temperature rises to 100ºC. When put in the oven an item is typically at room temperature. As baking proceeds, the internal temperature rises, and the product’s thermal conductivity theoretically increases because it has quite a bit of moisture content, and in fact it does rise up to a point, but then it drops long before it's internal temperature can reach 100ºC. Why is this? Despite the moisture content, other ingredients in the mixture aren't simple bystanders. Significantly, most bakery products include starch and protein; flour, pure starch, eggs, milk, and whey for example. At about 60ºC starches begin to gel, and soon afterwards proteins coagulate. Both of these developments affect thermal conductivity. The thermal conductivity of a baker's composite mixture decreases after about 60ºC.5  Because it's conductivity decreases, so does the thermal diffusivity of the item, that is, the rate at which it moves heat energy through the medium. 

From our meditations on density we know that expansion and moisture loss cause a material's density to decrease, which, for baked goods is a much desired outcome. We know that lower product density implies lower thermal conductivity and diffusivity, and it does so because the molecular structure of the item is more spread out. Conductivity is a molecule to molecule phenomenon. While it's certainly true that water becomes more thermally conductive as temperatures rise, such stuff as starch gelatinization, protein coagulation, product expansion, and moisture loss all get a say-so in how things get done in your cupcake. We cannot simply extrapolate that bakery items will resemble the thermal behavior of water when heated.6 Water will continue to increase in thermal conductivity up to 100ºC, but bakery items are not purely a function of their moisture content. Any bakery item whose formulation includes starch or protein will demonstrate lower thermal conductivity at above 60ºC. Can you think of any baker's formula, other than for making sugar syrup that does not include starch or protein? 

There is another important process phenomenon that occurs to complicate simple description. Even should these structural changes not impeded thermal conductivity, water would not continue to display an ever increasing rate of thermal conductivity. When internal temperatures rise sufficiently, water undergoes phase change, that is, liquid water turns gaseous; it turns to steam. When water vaporizes, guess what happens? The thermal conductivity of water plummets. This seems counterintuitive on the one hand, and just plain odd on the other. Wouldn’t something that’s hotter necessarily share that energy better? I mean, steam is hotter than water, right? Well, actually no, it is not. Steam is 100ºC, as is liquid water at its hottest. So, how on earth does The Unabaker ever get his burrito baked if it no longer has much conductive oomph, and why does baking nevertheless proceed increasingly more rapidly at this point? If conductivity plummets, would not baking become ever so tediously slow?

In some other universe, perhaps baking is more instantaneous, but in this one, baking is a gradual process. The density of a baked product decreases during the process because water content is continually being lost, interior structure starts to form, porosity develops, and the thing simultaneously expands. As it expands, the material’s molecular structure spreads out. Consequently, it takes longer to transfer energy molecule to molecule. Does the increased thermal conductivity from the rise in water temperature cancel out the decreased thermal conductivity due to lower density as baking progresses? If expansion was prevented somehow, would composite thermal conductivity stabilize, or perhaps increase? What compensates for the dramatic downfall of the thermal conductivity of water at phase change?

In fact, preventing expansion does matter, and it's an interesting topic for a follow-up article, and yes, the rise in temperature implies an increased thermal conductivity for products with higher water content, but phase change has a dramatic effect upon the process, albeit in surprising fashion. There’s something else afoot during the phase change of liquid water to steam that allows the process to carry on.        

Phase change is another really cool feature of water, but one which is so commonplace that we are almost immune to admiring such near magic as vaporization. What is it about water that makes it even less efficient at conducting thermal energy at the boiling point, and beyond? What it is, is the fact that gaseous substances, as noted earlier, have very, very low thermal conductivity. Let’s think about it. A gaseous substance has very, very low density. This means the molecular structure of a gas is widely dispersed. Nevertheless, conduction remains a direct, one on one relay event. It becomes harder to conduct the energy.

Imagine how many people a politician can shake hands with if the auditorium is vastly expanded, the exact same number of folks attend the rally, but they’re now spread out all over the room? Well, an overly earnest one can shake all the hands of course, but it would certainly be a very gradual process, and the old rascal would likely tire of trying, opting instead to just kiss babies in the front rows. Unlike aging politicians however, baking is relentless. It doesn't stop shaking molecular hands, but it does require more time and energy.

What about the type of material under consideration? Bakers fabricate all kinds of different stuff with all kinds of material properties. Some quite goopy, others dense as can be. Some fatty, others lean. Some are really airy, others liquid. Some with lots of egg, others with none. Some are quite sweet, others barely so. The type of material, and its current phase state makes a big difference to thermal conductivity. Solid materials are most efficient, most thermally conductive, then liquids, then gases, and almost any material, no matter what phase it’s in (solid, liquid or gas), is more efficient at conducting thermal energy when colder…except water.7 But water, even when it heats up, is still a very poor conductor by comparison to almost any other substance, and eventually, as we now know, it gets much worse. Water vapor is gas. This is why the thermal conductivity of water at phase change plummets.

What are the implications of this for bakers? For example, if The Unabaker makes a batch of baguette dough, proofs it overnight in the refrigerator, and puts it straightaway into the oven the following morning. Here are a few questions that come to mind, some rhetorical, others simply the sorts of things that Unabaker in his limited wisdom ponders:

-Water has lower thermal conductivity when colder. Because Unabaker’s baguette dough is cold, will it possess lower thermal conductivity, than a similar batch of dough that’s been proofed at room temperature before baking? 

-Because bread has a lot of water, and water has increased thermal conductivity when it gets hotter, doesn't this imply greater thermal conductivity during the first stages of the baking process despite the chill?

-Does chilled dough bake quicker than room temperature dough, the same as room temperature dough, or slower than?

-The thermal conductivity of baguette dough is just one of its properties. How do density and specific heat of baguette dough come into play? 

-All baguette dough is not the same. Perhaps Unabaker decides to use more water to make a new batch, and again, proofs it overnight in the fridge. More water means it’s more solid, right? Which means it has greater thermal conductivity, right? But, it also means the dough is more dense because water is more dense than flour. So I wonder, is the dough more conductive because it’s more solid, or more conductive because it has greater density, or both. 

-On the other hand, since water has very high specific heat, this means that Unabaker’s wet baguette dough has higher specific heat than does a drier (less hydrated) dough. Higher specific heat means that it takes longer to heat it up than would a traditional baguette formula that uses less water. Isn’t “taking longer to heat up” an indication of less efficient thermal conductivity? 

-We also know that water becomes slightly more efficient at thermal conduction as internal temperatures rise. Does that mean wetter dough bakes  quicker?

-If we consider that this baguette dough is both more wet and cold when put in the oven, what then? More wet means it either bakes up faster because it has increased thermal conductivity as the process progresses, or it means it has less thermal conductivity because it is cold, or perhaps being more wet, it's more dense, and therefore density trumps coldness.

-Colder usually means it has less thermal conductivity because water is less efficient when colder. Does cold, but wet dough mean that thermal conductivity is about the same? 

-“Wet” implies it will take longer to heat up, and presumably longer to bake, but it also implies more thermal conductivity as it heats up, which presumably means the process should quicken as it progresses. 

-Does a wetter dough profit more or less from cold overnight fermentation than drier dough? 

-What effect on energy usage does the temperature of the dough have? Does cold dough help to conserve total energy required for baking, or does it consume more energy?

-Does it always follow that denser dough has greater thermal conductivity? How does the total formulation, such as the type of flour, or fats, or eggs, or sugar effect thermal conductivity? Bread is a composite. Despite the link between water content and the various thermal properties, is it sensible to focus just on water content?

-Wet dough also implies that there’s more evaporative loss during baking, which implies more steam has been created. Steam is gas. What does phase change do to the process? 

-Steam has a small fraction (about 3.6%) of the thermal conductivity of liquid water that has been heated to just under the boiling point.8 From one moment to the very next, conductivity face plants. How does this affect the overall heat transfer phenomenon? 

Are you confused? So am I.9

So let’s talk about why the baking process carries on despite all. While it is absolutely true that steam is a dramatically inefficient thermal energy conductor, this doesn't mean that it's an inefficient mechanism of heat transport. Understanding the difference between the thermal conductivity of steam, and its role as a heat transport mechanism is crucial to getting to the heart of what's going on in the baking process. Discussing how so is in the on-deck circle; the next two chapters.

What’s happening when water content changes to steam? Does all the steam simply evaporate through the product surface? What about the condensation fractions that form as steam passes through the cooler areas of the medium? Does any part, most of it, or all of it act upon the yet uncooked mass? Let’s illustrate what’s meant by condensation fractions. Condensation occurs whenever steam comes into contact with a surface that’s less hot. Put your hand above a pot of water, and heat the water. Vapor rises, and strikes the palm of your mitt. It condenses. Your palm is wet. This is what happens inside your cake when baking. “Heat rises” is a truism, but it’s an example of a not precisely true truism. Why is that? It rises for a reason, but not because it's the destiny of steam. Steam is heat, and it sometimes does rise, but not necessarily so. The only reason we think that steam always rises is because we see it doing so from our cups of coffee, for example, or from a pot of beans simmering in our golden pot. It rises not because it is lighter than air, it’s not. It’s actually heavier than air. Since it’s more dense than air, why then doesn’t the air just sit on top of the steam? It rises because steam is heat energy, and heat energy always moves from the hotter region toward a cooler region. The air above your coffee cup is cooler, thus steam rises from a cup of hot coffee. Inside your cake, it’s a different matter. The inner, yet unbaked geometry of the cake is cooler than steam. Steam will go there regardless of whether "there" is up, down or sideways. When it does, it condenses on this region. What does that mean for the process? Condensation is an interesting process phenomenon. We’ll get to it soon.   

Thinking about coffee always gives The Unabaker pause. He desires to not stop thinking about coffee, so he proposes a short detour. Knowing that air is a poor thermal conductor, and that milk foam for a cappuccino is really just a bunch of airy stuff, which, except for it's preferable organoleptic properties, is much akin to styrofoam. When milk foam is put on top of your coffee can you see how this acts as an insulator? It's the same as putting on a puffy coat, right? If we brewed two precisely similar amounts of coffee directly into two exactly similar china cups that have been preheated to the same degree, and immediately topped one with a layer of milk foam, then tested both after 3 minutes, which coffee would be warmer? Obviously, the one wearing the puffy jacket right? Now, back to the story.

All substances have some measure of thermal conductivity. Ingredients are substances, but when mixed together they form what food scientists refer to as composites, colloidal mixtures of solids and liquids. It's true that thermal conductivity is an intrinsic property of matter, but it’s not an intrinsic property of composites. Instead, for composite mixtures, thermal conductivity is always some fraction of the thermal conductivity of the individual ingredients used to make it. That fraction will vary according to proportions of each ingredient used. This makes it impossible to extrapolate what happens in chocolate cake just because we know what happens in carrot cake. A further complication is due to the presence of large amounts of water in bakeshop formulae. Thermal conductivity is not well understood for liquids. Precise values for thermal conductivity of bakeshop composites are hard to know. Even if we know the thermal conductivity for the individual materials used, flour, water, eggs, oil, sugar, and salt, bakers mix these together in all manner of proportions to create a vast array of colloidal stuff, all of which possess varied density, and specific heat capacity. Baking is not a simple process. Understanding the process requires testing each type of product. No one ever thinks of colloids as particularly tasty, but because there are such benevolent beings as bakers, there’s a wide range of such things that are. Baker's call these things lovely names like Croissant, Savarin, Mousse, Pavlova, Cannelé de Bordeaux. All of which, as it turns out, are crucial to World Well-Being!

Composite mixtures undergo various process phenomena when baked. “Process phenomena” is another fancy pants phrase, but it just refers to the things that happen during the baking process. For example, the gelling of starch, coagulation of protein content, the movement of heat and moisture, the phase change from liquid water to steam, and since steam is a leavening agent, it also means that it aids product expansion, and the development of interior porosity. These things that happen affect the material properties of composites. Those properties, density, specific heat and thermal conductivity, change. Scientists study these process phenomena to find out the details, but Unabaker prefers simple illustrations. When you cook batter, there’s a lot more going on than when you cook water. This is pretty easy to grasp, but even for lab folks, moisture movement during baking is not so clear cut. 

Being an erstwhile Chaos theoretician, The Unabaker wonders, since steam and the motion of water is involved, might an element of chaos be involved as well? Chaos is a philosophical concept, and of Physics as well. Chaos refers to natural phenomena that exhibit turbulence. Things like churning water, smoke rising from a match, eddy flow. Turbulence is not an easy thing to explain using traditional mathematics and physical laws. To try to do so, mathematicians developed fuzzy logic, a sort of maybe yes, maybe no, neither entirely true, nor false type of probability logic. Can we hope to do better than to fuzzy-logically explain baking? These are the sorts of questions that require Unbaker to lie down on his couch.10

Why do we want to know about the thermal conductivity of batter, or dough, or pie? Because it's one of the fundamental properties of the baker’s composition. Arguably, bakers should understand in broad terms what’s going on, by which I mean, understand the process phenomena (things that happen), that make baking custard a very different process than for cake, or cookie, or bread. For commercial baking operations, understanding thermal conductivity is important for all manner of food processing: freezing, canning, and other packaging. Scientists also use this information along with data about other properties of bake shop formulations to design improved products, improved baking specifications, to design energy efficiencies and better baking technology. 

While this may not be of interest for the home baker, or even small operators, it's crucial to larger food processing operations. Besides all of that useful stuff, knowing more about what’s afoot during the baking process is just part of the pathway, the ever upward arc of the learning curve, adding nuance to our appreciation of what we do. Baking is about sustenance, but more so than that, it’s about emotional well-being. If you'd like the world to be a better place, then learn more, bake more, bake better. People will admire you. 

The formula for calculating the thermal conductivity of a solid, for example, is:  K=Qx/A△T. 

K = thermal conductivity; Q is the amount of heat transferred as a result of the temperature difference; x is the perpendicular distance between two isothermal planes under consideration; A is the area of the cross-section of the material; △T is the temperature difference between the two isothermal planes under consideration. 

[Isn’t it clear why bakers don’t calculate thermal conductivity of baked alaska and pop tart, and why would they? Note also, that the formulae for calculating density, specific heat and thermal conductivity get increasingly more complex, none of it horribly so, but none of it an essential part of a baker's day. Instead, thankfully, it gets done by food scientists worried to ensure that Unabaker can focus on warming up his boots more efficiently without distraction from having to perform burrito material property testing. One thing at a time is how The Unabaker likes it.]

2, January 31, 2019 

According to the thickness of the material, thermal conductivity can vary. For the following examples, we will assume that all materials are one meter in length, and the difference in temperature between one side and the other used is 298K (25º C). 

Thermal Conductivity of Copper           386 W/mK.
Thermal Conductivity of Aluminum       205 W/mK.
Thermal Conductivity of Liquid Water   0.606 W/mK.
Thermal Conductivity of Air                   0.02624 W/mK.

3 While not being central to our discussion of the basic properties and processes of the baker's craft, it is nevertheless an important part of The Unbaker episteme that baking fosters World Well-Being. The notion that such stuff as food can be either good or bad is a popular point of discussion, therefore it makes sense to wonder about various activities for making food. Among such, is not baking generally deemed to be virtuous; an example of the Buddhist notion of Right Action? Were bakers not allowed to bake, would not the World Well-Being Coefficient decrease? If baking itself is Right Action, then it's relevant to wonder about the virtue of baker's ingredients. Is there such a thing as good stuff, and bad stuff? We read about this all the time, and I think it safe to say that among things most folks concede to be good, is water, despite being such a crappy thermal conductor. 
The Unabaker ponders stuff like this. It's his duty as eminent Gastronomer. He understands that all things have various material properties. Is virtue among such? We know water has certain density, specific heat and thermal conductivity among other features. We know it tends to vaporize if we apply heat to it, but can stuff such as water, or flour, or sugar, or butter be in and of itself, either good or bad? Unabaker thinks not. The goodness or badness of these sorts of things, and the composites made from them is wholly a matter of their functionality, but again, in Unabaker's world, functionality necessarily includes delight. For humans, can we separate pragmatics or utility from desirability? If so, can we sustain doing so? Can any system of axioms for collective well-being exclude what we so fundamentally depend on for equanimity; moments of delight? I'm not suggesting that a chocolate eclair is the same thing as "thou shalt not invest unwisely", or "honor thy civic leaders", or whatever your basic code of conduct includes, but Unabaker suggests it as metaphor; a simpler apprehension of one's duties, and more compassionate understanding of others. He recommends sharing the eclair with someone you don't know.
Everyday we make judgments about things. What we eat seems to be one of the things we are most prone to consider. For example, we would say it's good to eat croissant, especially if very hungry, or bad to eat it if we have an allergy to certain of it's ingredients. Water is good to drink, bad to waste. Good for use as a solvent, bad for use as thermal conductor, but even though it's an inefficient thermal conductor, this very inefficiency makes it good for other things. The notion that things are good or bad is contingent upon many variables. As for baking, we might argue that it is neither good, nor bad, it's essential. 
Food morality is a popular motif of current thought, but this is because humans are doing the thinking. Subtract us, and what's left? In the natural world, goodness and badness do not really exist per se. Stuff is pretty much just as stuff is. Skies can be clear and blue, or bilious and opaque. Water might be pure, and the sound of it lovely as it trickles down a mountain trail as we hike by, but it doesn't matter to the universe, and without us, one has to wonder, is sound lovely at all? If water was sulphuric and nasty, or prone to random explosive activity, screeched as it moved, or otherwise just had a very bad attitude in general, it would not matter to the Earth, let alone the universe. Subtract us, and our needs and concerns, and what's left? There would be zero value judgements being made about stuff. If we imagine, there be other creatures in the universe with similar cognitive capacities as us, would they necessarily share our concerns, and needs, and our values? 
Stuff is neither good nor bad. Stuff is pretty much just the way it is until something makes it not that way anymore. Changes to the stuff of the physical world are results of other things in the physical world acting upon stuff. Setting aside human hopes, and dreams, and imagination is hard to do. We are but human, and dreams are useful too. Nevertheless, things are quite a bit different than we have traditionally imagined. Bakers are examples of stuff that happens to other stuff to change it. Are the changes we impose good or bad? Do you yet imagine what The Unabaker thinks?
This is why science is a useful tool. In addition to utility, Scientific inquiry is humans at their most imaginative, but it's a brand of imagination that can be tested. What's imagined has to adapt to what turns out to be true, and true is defined by Science as being both independently confirmable, and capable of accurately predicting other things that will occur if certain conditions apply. Science is a very, very creative enterprise. Besides uncertainty, what else describes humans? Among many things, it's our propensity to do things like imagine why. Science gives us answers to that question, but the answers don't rely on traditions of thinking or feeling. Scientific answers for why stuff happens or does not happen are said to be true if they can be expressed mathematically (an optimal condition), independently observed by other humans, and either independently confirmed, or disconfirmed by those others. Being confirmed or disconfirmed, true or not true has nothing to do with being either good or bad. But some stuff that Science helps us to know have practical, useful, aesthetic or otherwise beneficial impacts upon us all, and which we are accustomed to think of as good or bad.
 We know that water is neither good nor bad except in relation to its usefulness to us, and that the concept of "usefulness" does not exclude ability to provide pleasure. In this respect, water is perhaps the kindest of all things since we have so many things we use it, and need it, and admire it for. If you like to express your appreciation for things through the lens of human morality, then it's certainly so that water has many redeeming virtues, some strictly aesthetic, but most of the ones we rely upon are practical. Even though it's a crappy conductor of thermal energy, this very feature makes it perfect for lots of things. If one looks at tables of conductivity for common materials, water, because it’s such a prevalent earthly material, will always be listed, even though it’s a very, very inefficient thermal conductor. Precisely because it's so, and because it’s readily available, and because it has very high specific heat capacity, people like nuclear power plant operators use lots of it to cool the working innards of their workplaces. It's what science folks call a "sink" can absorb an awful lot of heat. Thus it's used often as the "cooler" region to which heat energy will always flow. We do this for really good practical reasons, not because water has been bad. 

4 This is not precisely true. Different materials respond differently to pressure changes. Solids and liquids aren’t too much affected, but gaseous substances such as steam, are. Why? Because increasing pressure compacts the gas. Compaction moves the molecules closer together again. Being closer means conduction takes place more readily. The thermal conductivity of steam increases when pressure increases.

5 Thermal Diffusivity Measurements of Wheat Flour and Wheat Flour Dough, Gupta, T.R., (2007), Journal of Food Process Engineering, 19, 343-352, 10.1111/j, 1745-4530, 1996

"It was found that thermal diffusivity of dough increases with moisture and temperature below 60ºC, but above 60ºC its value decreases. This is attributed to physico-chemical changes, e.g., starch gelatinization and protein coagulation. Due to these changes, swelling and softening of dough occur, which reduce the ability of dough to diffuse thermal energy, thus lowering the value of thermal diffusivity."

[The Unabaker has extrapolated that a corresponding decrease in thermal conductivity occurs for the very same reasons, at the very same temperature during the baking process, and which correspond also to notable changes to density, moisture content, and product geometry. Three things affect thermal conductivity, temperature, moisture content and density. In this case, all three combine.]

6 In fact, there are other things that happen; other process phenomena that make this a not directly proportional relationship. For example, density of a product changes due to expansion and porosity development, both of which inhibit efficient thermal conduction. Starches gel, trapping a lot of the moisture content of the formula within its matrix. Less moisture is available to transport thermal energy, and both starch-gel matrix and protein coagulation impede. 

7 This is a very simple description of how temperature alters the thermal conductivity of a substance. Metal solids, and non-metal solids react differently to temperature change, and component materials (i.e.collections of materials, such as alloys which I think stuff such as cake batter might be analogous to) are different as well. Since bakery preparations have large amounts of moisture, it's reasonable to expect the thermal properties of various preparations reflect to some degree the thermal properties of water. The description given is only intended to broadly inform about the idea of thermal conductivity, and since The Unabaker is trying to understand this stuff just like you, broad descriptions are sometimes preferred. 

8 The thermal conductivity of water at a point just above freezing is about .555 W/mK, and at the point just prior to boiling, it has increased to about .677W/mK. At the point of phase change to steam it drops to .024W/mK, and then rises incrementally as the temperature of vapor rises (which requires increased pressure to do). Why then does the baking process not stop? The answer is interesting.

9 Considering the massive energy requirements, and the goofy science stuff that has to happen to bake pie, pasties, bagels, genoise, and all that other fancy stuff, and the confoundingness of it all, it's starting to seem like baking is just a massively inefficient and unfathomable cooking method. Consider the following:

-What's the relationship between total world ingestible calories produced by bakers versus total heat energy calories used by bakers? Are we coming out ahead? 

-Can we feed more people by eating less tarte tatin and tater tot; switching to more efficient, and easier to understand cooking methodology? We could eat more porridge for example. 

-Is there sufficient link between consuming tasty pastry and crusty bread, and a higher World Well-Being Coefficient? If so, does it outweigh the inefficient use of energy required to generate the added degree of WWB? 

-The Unabaker tends to ponder stuff, and has often been observed thinking too much, i.e. lying inert on couch. As The Unemployed Philosopher’s Fair blue ribbon holder in Ethics three years running, well regarded by peers for his discerning treatises on the nature of Good and the Not So, Unabaker wonders, to save our planet, shouldn’t we just quit baking? Formulating the argument for consuming more stir-fried rice and tortillas, ice box cakes and stove top puddings was not a straightforward piece of critical thinking! 

-How does a million unemployed bakers factor into improved world well-being? What does one do with excess bakers? Retrain them to make kimchi and kombucha? 

[Rising from couch in this immersive meditative state, The Unabaker realizes it was just a crazy food dream. Off he wobbles to make his coffee, after consuming which, it occurs to him that perhaps there's something else about steam and thermal energy transfer that he needs to know. In the interest of saving perhaps millions of baker’s jobs worldwide, Unabaker vows to think about it, and report later. He feels a sense of urgency and responsibility.]

10 It’s perhaps hard to believe, but there are smarter theoreticians than The Unabaker. One such is particularly noteworthy for a couple things. Werner Heisenberg won the Nobel Prize in 1932 for helping to found Quantum Mechanics, the study of the most minute features of physical reality, the quantum world of sub-atomic structure and particle behavior. Herr Heisenberg is most famous for saying he’s unsure of stuff. Imagine that? In this regard he’s my hero because, if there’s anything that describes The Unabaker, it is lack of certainty. 
Whereas Unabaker is merely uncertain, Mr. Heisenberg actually postulated uncertainty as the best we can know about some important features of our universe. He made being unsure a foundation of modern Science. The Uncertainty Principle is a basic assumption in the realm of Quantum Physics. 
The other thing I like about this fellow is the apocryphal story (which means it might be true) that has quoted him to say, “If I meet God, I shall ask him two questions, why Quantum Mechanics, and why Turbulence?” This story is poignant testament to the degree of confoundment that Science has for precisely describing what’s happening at the most minute levels of physical reality, and on the other hand, for such perfectly obvious features of the natural world as turbulence. 
Turbulence as a physical concept has mostly to do with the concept of flow, the movement of water, but also such stuff as turbulent air. There are all sorts of things in nature that exhibit turbulence, and which affect our lives directly, but these were notoriously hard to describe mathematically, or by using existing theory, and therefore quite hard to say precisely true or false things about. Fuzzy logic was a direct effect of this new “knowledge”. Isn’t understanding the movement of moisture during baking of similar difficulty as describing turbulence? Is the best we can hope for to describe the process “maybe”?
Heisenberg was also suspected to be a Nazi spy, and was indeed working on the atomic bomb for Germany, although he later claimed the explosion in his lab that upended the research was a ploy he devised to stall it. He was so important to that particular project that the United States at one point decided to assassinate him, but the assassin who followed him around for a while ultimately decided he wasn’t sure enough of Heisenberg’s role to warrant doing the deed. So it seems that uncertainty almost defines Herr Heisenberg doesn’t it? 
The upshot was that someone so prominent and famously uncertain was spared. Was this a victory for humility? We should all hope for the same benefit of the doubt. After all, is there anything more profoundly the case about the human condition as being uncertain?
At the next annual Phenomenologist’s Fair I hope it’s remembered, after my address, when most of my answers during the Q&A are “I dunno”, “I’m not so sure about that!”, and “It’s indeterminate”, that they gave Heisenberg the Nobel Prize for such lucidity. Famous for being unsure, Werner Heisenberg!


Thermal Diffusivity

Diffusivity is a fussy word. It just means rate of diffusion. Of course, diffusion is kind of fussy too, but it can be defined in this case as the phenomenon of the gradual spread of moisture or heat energy throughout a medium. For instance, how hot coffee seeps gradually across the tablecloth after my cup gets knocked over is an example of both heat and moisture diffusivity. Thermal diffusivity is like that, but specific to the spread of heat energy. It refers to the rate of thermal energy movement. 

What name we call a substance, aluminum, bauxite, hoppin’ john, water, egg, cake, custard or Unabaker is because each of these substances has a specific molecular structure and chemical composition. Material properties of substances are due to its structure and composition. It’s how we identify one from another. Walnut is different from Chestnut is different from Aluminum. Change it’s molecular structure or chemical composition, it's not called Walnut, it’s Walnut wood. We know that changes to heat and pressure applied to a material will alter its material properties, and so, the baking process alters the chemical composition and molecular structures of items being baked. Another silly example follows, using moisture instead of heat.

Adding red wine to sofa is a common phenomenon, therefore conceptually easy to grasp, so let's examine red wine diffusivity in sofa. We know that red wine diffuses in sofa quite readily, but we want to know the precise rate of diffusion. Since sofa is a large object with odd geometry, not ideal for diffusivity testing, and also to contain wine cost, Unabaker decides to test for cushion only. We might call our experiment something cool like “Modeling of Red Wine Transport in Mid-Century Modern Cushion”. To make the analogy fit the thermal diffusivity model better, let's imagine wine to be heat energy. How does red wine energy diffuse in cushion? It does so according to a specific set of conditions, namely, the amount of wine energy applied (one glass, two?), the mechanism of application (a drizzle from one edge, or simultaneously from all edges?), cushion density and geometric configuration (soft, hard, square, oblong?), and duration of wine energy application (one minute, two, ten?). There are other things involved too, but let’s keep it simple. 

We can directly observe the process of red wine diffusion in cushion, so it's relatively easy to do the measurements to calculate its rate of diffusion, i.e., its diffusivity. Even so, the calculation is valid only for mid-century modern cushion of specific material specification. Nevertheless, after testing, we could predict how much red wine to apply, and the correct time parameter required to treat other quite similar cushion. 

This silly example is nevertheless analogous to baking cake batter. Every type of batter is of different formulation, baked in various different geometric configurations, similar to the material specifications of cushion. Just as results for a specific mid-century modern cushion do not apply to wool carpet or leather chaise, testing white cake batter doesn't tell us much about yellow cake batter, and only in very broad terms does it illuminate the baking characteristics of custard or ciabatta. Understanding the baking process requires study and tests, mathematical modeling and diffusion equations to describe and predict process phenomena of all baked goods. Scientists are delighted to do that, and report to us, so we can just bake.

The movement of wine is analogous to the movement of thermal energy. As it diffuses, one thing we readily observe is a moving boundary between parts stained, and parts unstained, analogous to the regions of cooked and yet to be cooked batter. The size of the untreated region shrinks over time as wine application continues. The boundary line between stained and unstained cushion moves gradually through the cushion, and as long as the wine energy is applied it will do so continuously until a stable distribution is achieved throughout. At which point, our cushion could be described as done. 

It's not a perfect analogy because, the interior unbaked region of a pie or bread dough or cookie dough is a geometric shape subjected to heat from all sides. As a result, this geometric shape of unbaked material shrinks from all sides toward its center. Perhaps you can visualize what the geometry of unbaked stuff looks like in baguette dough versus cake batter. Because baguette is long and thin, the geometry of unbaked dough is like a cigar. In the cake it's a wide disc. Remember when we were wondering why the baking process speeds up as it progresses despite the plummeting thermal conductivity of the baked stuff? Well, as the process advances, the speed at which the boundary line moves will increase because there’s less and less mass of uncooked matter, but the same application of heat energy. And remember we discussed that moisture loss occurs mostly prior to crust formation? Well, there’s also less and less moisture to evaporate as the interior geometry of unbaked matter shrinks. As the geometric shape, and the dimensions of the uncooked mass shrink, the moving boundary of thermal energy moves progressively quicker. This explains why The Unabaker burns his toast so frequently. Busy making omelette, coffee, and other stuff, he took his eye off the toast. The toasting process takes a relatively long time before browning begins, so he's deceived into thinking he can get omelette from frying pan to plate, but then his toast goes from lovely pale caramel to char quite quickly. Bakers know, as the process proceeds, the quicker is the pace, especially in later stages, and for this reason experienced bakers go for coffee right after the batter goes in.

Geometry doesn't come first to mind when thinking about the baking process, does it, but it's absolutely fundamental. The geometric configuration of a product can be short, long, narrow, fat, round, spherical, oblong, square, triangular, rectangular, deep or shallow. Determining the amount of heat, and time required to bake cake batter depends not only upon ingredients used, in what proportions, and how these were mixed, but the geometric configuration of the cake pan used. Geometry applies as well to any other baked product whether or not it’s baked in a mold. A baguette, bâtard, or boule of the same dough formulation and same dough weight bake differently. Just as the geometry of an object is an important consideration for its thermal conductivity, so it is for thermal diffusivity. Geometric configuration affects the rate at which thermal energy can be conducted within the batter, and the diffusion (movement) of that energy. Geometry affects how moisture moves within as well. How so? Picture a jelly roll cake being baked, and the same batter baked in a brownie pan. The jelly roll pan is much wider, longer, and shallower. As a result, jelly roll batter has more exposed surfaces. It bakes more rapidly.

Thermal diffusivity is different from thermal conductivity, but the rate of thermal diffusion within a material, and the thermal conductivity of that material are related. The thermal conductivity of a material will affect the rate of thermal diffusion. Returning to my silly analogy, to understand wine diffusivity for cushion, we need to understand the material properties of cushion. Has it thin or thick fabric, open weave or dense weave? Is it made from wool, cotton, silk, or leather? All of these properties will affect the conduction of wine energy, and the rate of wine energy diffusion. Heat energy is able to diffuse through cake batter at a specific rate on account of (among other things) the geometry of the item, the composite thermal conductivity of the ingredients used in the formula, and resulting porosity after mixing. Mixing adds air, and air implies porosity. As we know from our meditations regarding conduction, porosity makes a big difference. The amount of space between molecules matters. Bakery products use vastly different proportions of similar ingredients, requiring different methods of mixing, some of which purposefully incorporate air. Thermal conduction within, varies accordingly; airy ones being less conductive than denser ones. Air is a well-known thermal insulator. It inhibits conduction. Besides the exterior geometric configuration of the item being baked, an airy substance like cake batter has very different internal geometrical structure, which we more commonly refer to as molecular structure.

The rate of diffusion of heat energy depends on a material’s thermal conductivity. A material that is a more efficient thermal conductor will normally have greater thermal diffusivity. Water is a better thermal conductor than flour. Other factors are involved. Density will affect the rate of diffusion. Water is more dense than flour. Specific heat capacities of water and flour will affect things. Water has much higher specific heat than flour. Differences in density, specific heat, thermal conductivity, and thermal diffusivity all come into play if we are trying to determine the overall baking characteristics of a specific product.

Why do we want to know this stuff? Because it’s what's happening when we bake. We want to determine ideal bake times and temperatures for all manner of delicious stuff. There are many practical applications of this knowledge in the food processing industry. 


Moisture Diffusivity

Understanding the concept of diffusivity is important, but what we really want to understand is how it works. Measuring it is cool, but what's going on? Since heat and moisture transport are what the baking process is all about, understanding the mechanism for this is a focal point of research. We talk about these together since they happen simultaneously. 

To use two trite examples of the complex, we think of stuff like brain surgery or rocket science, but in its own way, baking is very complex, and some of what goes on, particularly as regards moisture transport is not well understood. Do you think we could land on the moon if we didn’t understand about trajectory and synchronous motion of planetary objects pretty well? While it may not be rocket science, baking is not so very simple.1 Not fully comprehending one of the most important process phenomena at work in the baking process, how on earth do we get it done?

One focal point of study for understanding the baking process has been to determine the precise mechanism for heat and moisture transport, because these two things pretty much sum up the whole process. Scientists want to be able to make useful predictions that allow us to better formulate products, to do so more efficiently,without the wasteful expenditure of human time, energy consumption and ingredient cost involved in trial and error testing. Throughout the history of baking, trial and error was the available methodology bakers had for designing new product. Food science studies of the baking process are geared not only to design new product, but to do so predictably and efficiently.

What do we know about the primary mechanism of heat and moisture transport during baking? Conduction is obviously involved, but is it the prime mover? It was generally assumed to be so, since it’s how heat is transferred on the molecular level, but in fact, process modeling has shown that what happens when liquid water turns to steam, namely evaporation-condensation, is the major transport mechanism.2 Condensation occurs not just on the exterior surface of the product, it occurs as the steam acts upon any cooler matter, which includes the yet unbaked interior geometry of the item. It's what scientists are keen to understand, and be able to predict.

This seems to conflict with what we know about thermal conductivity of water. When water turns to steam, thermal conductivity plummets. We also know that the expansion of the baked product makes it less dense, more porous. Porosity inhibits thermal conductivity as well. Water isn't the only ingredient that undergoes phase change. Fats present will melt, also making batter or dough less dense. It's known that moisture diffuses more readily through dense formulations than ones with greater porosity, but thermal conductivity and diffusivity are not the same as the actual mechanisms of mass transfer.  

What accounts for the action of steam evaporation and condensation to influence heat and moisture transport? At phase change, water has what science calls “infinite specific heat” since all of its energy is going into the change. We also know that the density of water is far lower when it manifests as steam, and even though the temperatures of steam and boiling water are the same, what isn't the same is the total amount of heat energy in steam. Steam has much greater heat energy than does water near the boiling point; about nine times as much. It takes a lot of energy to heat up water and then turn water to steam. This is called the latent heat of vaporization, sometimes also called Enthalpy. Steam carries that heat energy, releasing it upon condensation. This is why heat and moisture transport go hand in hand. While some of this energy is released to the oven chamber as evaporative loss through the product surface, much of it is transferred within the product toward the unbaked center, condensing on cooler matter therein. A significant fraction of the original moisture content of the formula is retained, bound in the gluten starch matrix, while the excess is simply eliminated in the process of evaporative loss. Since steam occupies much more space than water, and carries much more heat energy, phase change is like a bomb going off inside your cake batter. The energy in that bomb is released upon impact with any cooler matter within.

As noted, moisture diffusivity is not well understood, least of all by me, but I can visualize the force of steam acting upon the product, and understand that it carries much greater energy; the latent heat of vaporization. It’s enough to make dwindling thermal conductivity a dwindling factor. The actual conductivity of steam may be very low, but there's a lot more energy being applied as condensate. Thermo-physical changes to the product inhibit conduction, but phase change adds many multiples of the heat energy. Knowing that it takes a lot of energy to heat up water (because it has very high specific heat), it makes perfect sense. We understand from the First Law of Thermodynamics that energy doesn’t vanish, it just goes from one place or form to another. Much of the caloric energy required to heat water to the boiling point, the point of phase change, was lurking in the heated water. This is why it’s called “latent”. It required just a lot of energy to cause phase change to steam, and condensation to unleash it all. 

Gaining a general notion of what’s up with the properties of density, specific heat, thermal conductivity, and the process phenomena of thermal and moisture diffusivity illustrates what drilling down to discover the intimate details of the baking process can provide. All of this discussion is by way of introduction to the more interesting stuff that follows. We aren’t scientists, we are bakers. A deeper understanding without too much drilling is good enough. To get to that, it’s useful to understand baking as a moving boundary problem.

1 While the following example doesn’t shed specific light on the mystery of moisture transport in the baking process, it may provide a bit of amusement. I’ve used it frequently over the years to illustrate what cooks and bakers do for a living, and how it’s done differently by each, neither of which activity is what I would call simple, but for different reasons. 
Making light bulbs, on the other hand, is relatively simple stuff. An order is received to buy x number of units. The raw materials required to make bulbs sit on shelves in the inventory. They can get dusty, but almost never spoil. The production facility is already set up to make a wide range of bulb types. Machinery has settings to produce the various parts, and other machines fit them together. Thousands can be made in a single run, each one virtually identical because the raw materials always adhere to a rigorous standard of specifications, and the machines can replicate each step in the fabrication process with great precision. But in fact, light bulb makers rarely fabricate to order. Bulb makers always have a warehouse full of all types of bulbs just waiting for a customer. Upon receipt of an order, all that's required is someone goes to fetch ‘em right off the shelf. The order is assembled, and shipped. Special orders can be filled, but it takes extra time, and costs more of course. 
By contrast, kitchens are more like your town’s humble little mattress factory. “We make ‘em in the back, and sell ‘em up front”. Nothing’s made ahead that’s fully ready to deliver to a buyer. There’s no warehouse full of Crispy Duck Tongues in Chengu Bean Sauce sizzling on a shelf waiting for duck tongue eaters to arrive. Instead, dozens of customers sit out in the salesroom waiting for their orders to be fabricated within 15 minutes of having placed them. Every eater orders what they like, and whatever that is, the factory team is expected to be ready to fabricate it from start to finish, plate it up, and get it delivered pronto. Manufacturing specifications certainly apply. Chef makes sure, but these are hardly akin to precision work…leeway exists. In any case, eaters are constantly setting their own specs. 
I remember as a young chef, my Chef telling me that there are only 3 degrees of doneness: well done, medium and rare, all else is metaphysics. But how about the fellow that likes his steak done Pittsburgh style, but only on one side, or my mom who would be horrified by the presence of “juice” in meat; the gourmand who imagines the land of rare to mid-rare? Of course, with thermal circulators to precisely dial in any degree of doneness, it’s not metaphysics at all. It’s do-able, but not on the fly. One needs notice. Kitchens aren’t blessed by such a thing.  
A roomful of eaters will typically have ordered a wide variety of things, which is the first order of added production complexity. The second degree of which is that quite often what’s ordered is stuff that’s not made by the factory at all, and the third degree of it occurs when the non-existent, is compounded by the goofy; additional special requests such as…”I had lunch at a cute little place in Rosarito five years ago, and had the absolute best fish taco there. It was kinda crunchy, but creamy, and had a really tasty slaw made from, hmmm, I’m not sure, but really tasty…and I’ve asked maybe 20 different restaurants to try to make it just like I remember, but no luck so far…can you ask Chef if he can do those for me?” And then, the next table orders some other fondly, but dimly remembered dreamy concoction, also not made back in the factory, and of course, both dreamers expect not to wait much for their special order to be fabricated, nor to pay more for it. They’re hungry, they want it right away! 
Meanwhile, lots of stuff is happening unpredictably back in the plant. The broiler just stopped; a cook burned a hand; a server whose lover just canned him has dropped a plate of food, and now, that entire table will be delayed while the dropped plate of duck tongue sizzle gets fabricated again. The plant’s production supervisor is what we call the Expo. The expediting chef has to be like a conductor and choreographer. His job is to figure it out so that all of this different stuff gets fabricated in sync, and each table’s order can be assembled, and shipped in one go, PDQ. He’s expected also to do this without earnestly communicating at the lovelorn server. It’s so not easy!
Now imagine this sort of business model applied to your local symphony. The orchestra conductor is much like the Expo, controlling the pace of the production, but what if the audience was allowed to shout out special requests, goofy stuff like…”hey I really like this Mahler piece, but I always wondered what it would be like if Debussy had written it, can you do that?”, or another barracks…“I prefer it in D minor, okay?”, someone else…”I heard this same piece last winter in Berlin, and this isn’t what I remember at all!”, another guy adds…“this here part is kinda boring me, can you pick it up a bit? You know, a little more allegretto, huh?” 
Being Expo can be quite a rush, and loads of fun, or it can be a bunch of absolute nonsense. Cooks use lots of different very perishable ingredients, most of which are liable to change day to day in important physical respects. Cooking it to order, while accommodating special requests, with the added chaos of having actual people making stuff instead of machines; it’s not like making light bulbs at all. 
Baking by contrast avoids much of this sort of kitchen mayhem, though not all of it, and it’s why bakers are bakers. Some of us prefer to be alone, tidily out of the fray, merrily fabricating sweet things, increasing World Well-Being bit by bit. Baking requires a different approach. Chaos has to be eliminated as much as possible, and of course, the cooking methodology is much, much more precise than the degree of finesse that line cooks normally observe. Cooking is easier in many respects, not so easy in others. Do you think that the dimly remembered fish taco is somehow more clearly imagined by a busy line cook who doesn’t normally make taco? Line cooking doesn’t provide spare time for much thinking. It’s a doing, not doing, zen sort of flow. It can be kind of brutal when really busy. I used to tell ‘em, “Nobody here’s paid to think, but me. You, just cook!” The appropriate response was, and always will be “Yes Chef!”.
Bakers are like lab workers, focused on their formulae, carefully scaling out required amounts of ingredients, and being mindful of the mixing. They also have the luxury of making batches; 10 or 20 of a thing at a time. In this respect baking is a lot more like factory work. In fact, bakers actually do have little warehouses, called walk-in refrigerators, to store parts and supplies; ready made components, which can be assembled, and finished over the ensuing few days according to generally predictable par levels for each day’s expected requirements. There’s not much “made to order” action going on. Only in the dessert station is there anything like what the line cook suffers. 
Nevertheless, bakers and pastry chefs get their fair share of special requests. I could tell a hundred tales of such, but here’s a memorable one. Once, at an internationally renowned establishment I happened to Chef, a famous guest brought me a Fabergé egg, not as a gift, but as example of the sugar and Pastillage ornament she desired be made to top her wedding cake. “Can you make this for me Chef?” Well, of course we can, and did! 

2 Modeling of Simultaneous Heat and Water Transport in the Baking Process,  S.S. Sablani, M. Marcotte, O.D. Baik and F. Castaigne, LWT - Food Science and Technology, Volume 31 (3) - April, 1998


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