#### This course supplements other food and science books by offering a quantitative and visual way of understanding the basic physical and chemical transformations that occur to food during cooking.

##### There is a wealth of information about food and cooking available. This book will give you a quantitative and visual framework for seeing underlying patterns, by making fundamental scientific concepts more vivid.
###### What can I learn from this site?

This set of lessons is designed to teach a more a scientific way of approaching recipes, by asking what parameters, such as time and temperature, can be varied and discovering the effect these have on the final product.

###### What's not one this site?

The science of flavor and perception is fascinating, but can't be easily translated to cartoons and graphs. There are many thousands of chemicals, which interact with a unique set of receptors and neural pathways in each person consuming them.

• ###### Calculate the quantities from a recipe in terms of metric units, and check whether they make physical sense. Knowing how to work in the metric system will make quantitative calculations far easier.
• Converting between units is just like multiplying by one.

$$1 Pa = 1 \frac{N}{m^2} = 1 \frac{N}{m^2} \left( \frac{1 m^2}{10^6 mm^2} \right) = 10^{-6} \frac{N}{mm^2}$$

• Check the answer by comparing it so something more familiar. A few converions relevant to recipes are shown below, and the full list list is avilable here.

 English Metric 1 teaspoon 5 ml 1 tablespoon 15 ml 1 cup (8 fluid ounces) 240 ml 1 ounce 28 g 1 pound (16 ounces) 450 g 1 teaspoon 5 ml 1 inch 2.54 cm 0.39 inch 1 cm

Note that 1 ml = 1 cm3.

• ###### Calculate the answers to equations in terms of scientific notation.
• The number of significant figures denotes the accuracy of a measurement, such as 0.1g accuracy for the small black scales.
• The exponent denotes the order of magnitude of the number.
• ***

#### Molecules in Food: Food can be explained by the interactions between the atoms within molecules, or between the molecules in food.

##### Cooking was invented to improve the nutritional quality of food; the differences between cooking techniques for different foods is best explained in terms of the interactions between the molecules within the food.
• ###### Draw and describe the main types of molecules of food, in terms of structure, size, and hydrophobicity, and where they are found in food.
• Atoms are the building blocks of matter. There are over a hundred types of elements, but only a handful are used in food: hydrogen, oxygen, carbon, and nitrogen are the most common.
• Water is the most prevalent molecule in food. It consists of two hydrogen atoms attached to one oxygen atom. One useful way of categorizing molecules is how they interact with water; they can be attracted to water (hydrophilic) or be repelled by it (hydrophobic).
• Many of the molecules in food are chains of smaller units. The chains are called polymers and the smaller units are called monomers.
• Carbohydrates can be monomers, like glucose and fructose. These can form dimers, like sucrose, or longer polymers, like starches, pectins, and gums. These are typically hydrophilic
• Proteins are polymers of amino acids. Some of these amino acids are hydrophobic, some are hydrophilic, and some are neither. The protein folds in a way so that most of the hydrophilic parts are on the outside and the hydrophobic ones are on the inside.
• Fats or oils consist of three fatty acids attached to a glycerol backbone, so they are called triglycerides. The fatty acids can be saturated (straight) or unsatured (bent, due to a double bond in the carbon chain). They are typically hydrophobic.
• ###### Calculate the number of molecules of an ingredient used in a recipe. Many culinary reactions are best understood in terms of the number of molecules in the recipe, rather than the numbers in the recipe.
• Since there are so many molecules in any amount of an ingredient used in a recipe, scientists use Avogadro's Number, NA, which is equal to:

$$N_A = 6.022 x 10^{23}$$

One mole of a material has Avogadro's number of molecules.

• Using the molecular weight, we can calculate the molarity (moles per liter) of ingredients in a recipe, such as the salt in a soup. For this case, we used the molecular weigh of salt (58.44 g/mol). If there are g of salt dissolved in L of water, then then concentration is molar.
• ###### Give examples of the types of bonds that act between atoms or molecules:

Bond type Energy (kBT) Energy (J) Note
hydrogen 10 4.1x10-20 between water molecules
van der Waals 1 4.1x10-21 between molecules
ionic 2.5 1x10-20 between ions (in water)
covalent 200 8.2x10-19 within a molecule

from Physical Chemistry of Foods ed. by Pieter Walstra

In the context of this class, permanent bonds can't be broken by heating the food to normal cooking temperatures. For instance, the bonds between alginate strands (due to calcium ions) or between proteins (due to transglutanminase) are permanent, but the bonds between oil molecules are not.

• ###### Give examples of bonds that are rearranged during digestions to release energy.
• Energy is stored within the covalent bonds of molecules, such as the carbon, hydrogen, and oxygen atoms in a sugar.
• During digestion, these bonds are broken, and the atoms rearrange into different molecules.
• The total energy stored in the bonds of the resulting molecules is less, so the resulting energy can be used by the organism.
• The energy in a food can be approximated using the 4-4-9 rule.
• ###### Give examples of bonds that are rearranged during cooking to change the texture of food.
• Van der Waals bonds between triglycerides hold fats and oils together, but these bonds are broken when it is heated.
• Hydrogen bonds are important for how a molecule interacts with water.
• ###### Calculate the concentration of hydronium ions, given the pH of a liquid.
• The pH of a liquid is the logarithm of the hydronium ion concentration.

$$pH = -\log{[H^+]}$$

• Small additions of highly acidic liquids can have a major effect on pH:

While making lemonade, you add ml of lemon juice (pH = 2.0) to ml of water (pH = 7.0). As a result, the pH becomes and the concentration of hydrodium ions is mol/l, more conveniently written as 10- mol/l.

For context, you can compare this to the molarity of a typical salt solution.

• Show table of common food pH values.

***

#### Energy in Cooking: All cooking involves changing the temperature or manipulating the bonds between molecules.

##### Humans are the only species to use heat, acids, or salt to cook food; this allowed us to evolve larger brains and spend a much smaller fraction of each day chewing food, according to Harvard primatologist Richard Wrangham.
• ###### Give examples of how different cooking techniques, such as frying and blending, can transfer energy to food.
• The three main types of heat transfer are conduction, convection, and radiation. In conduction, the heat is transfered by microsopic collisions between molecules, whereas in convection, there is a larger scale movement of material, such as circulating water in a hot pot of water. In radiation, the thermal energy is transfered by electromagnetic radiation, such as in a microwave oven.
• An induction burner has a coil of wire, with an alternating electric current flowing through it. This causes a current to flow in the pot above it, as long as the pot is ferromagnetic. The pot isn't a perfect conductor, so much of the electrical current is turned into thermal energy, which heats the food. See the Wikipedia entry for more info.
• Heating transfers energy from a heat stove, like a stove or oven, to the food. This can be through a medium such as oil in deep-drying or water in steaming.
• Wet cooking methods, which involve water, can only heat food up to 100°C; dry cooking methods can heat food much higher.
• ###### Draw how thermal energy changes the motion and shapes of the molecules in food.
• Heat causes the molecules in material to move faster, as shown in the simulation below:

The thermal energy, U, of a material is related to the temperature of all of its molecules by Boltzmann's constant, kB.

• Uthermal = kBT
• kB = 1.38 x 10-23 J/K
• T = 300 K

When T = K, then the energy is x 10-23 J.

• Heat causes fats to melt; the melting temperature is higher for longer, more saturated fatty acid chains.

• Heat causes proteins to unravel, in a process called denaturation

.
• Heat causes starches to unravel, a process that chefs called gelation (but we won’t, since it has another meaning in physics).
• ###### Calculate the amount of energy needed to increase the temperature of a food by a particular amount.
• Specific heat, cp defines the energy required to raise the temperature of a material with a mass, m, by a specific amount, ΔT:

$$U = m c_p \Delta T$$

If a drink with a mass of g and a specific heat of J/(kg K) decreases in temperature by °C, then J of energy must be absorbed by the whiskey rocks.

• On a two-dimensional plot of temperature vs. heat added, a steeper slope implies a higher specific heat, such as in the graph below for water (4.18 J/(g K)) and oil (1.73 J/(g K)). In other takes more energy to raise the temperature of water by a particular amount, relative to oil. A table of specific heats can be found here.

• ###### Calculate the thermal energy of a molecule using Boltzmann's constant.
• The thermal energy, U, of a material is related to the temperature of all of its molecules by Boltzmann's constant, kB = 1.38 x 10-23 J/K:

$$U = K_B T$$

When T = K, then the energy is x 10-23 J.

For context, compare these to the table of bond strengths.

***

#### Phase Transitions: When energy is added during cooking, food can change in other ways that getting hotter; these changes are precisely the reasons why we cook food.

##### Phase diagrams can visually represent qualitative changes in the interactions between molecules, ranging from simple (e.g. boiling water) to complex (baking a cake).
• ###### Give examples of how steps in a recipe can change the interactions between the molecules.
• Acidity and salinity can affect the electrostatic interactions among the amino acids in a protein, causing it to denature.
• ###### Draw a one dimensional phase-diagram, as shown by the examples below from Dave Arnold.
• Eggs undergo numerous transitions, separated by just a few degrees in temperature.
• The color of a steak changes from red to brown, as the meat becomes tougher.
• Salmon changes from raw and toothy to overcooked and dry.
• The molecules in a material can turn into a gas above the boiling point (352 °K), as shown in the simulation below:

The thermal energy, U, of a material is related to the temperature of all of its molecules by Boltzmann's constant, kB.

• Uthermal = kBT
• kB = 1.38 x 10-23 J/K
• T = 300 K

When T = K, then the energy is x 10-23 J.

• ###### Give examples of reversible and irreversible phase transitions.
• Simple phase transitions, like freezing and boiling, are reversible. In other words, the state of the material can be entirely described by its position on the phase diagram. The material can be returned to its original phase by getting back to the same conditions (e.g. temperature and pressure).

image source

• More complicated phase changes, like cooking a steak, are irreversible; cooling the meat down does not make it raw again. The physical structure of the food has permanently changed.
• ###### Draw the path taken by food during various cooking processes, such as boiling, freezing, rotary evaporation, or pressure cooking, on a pressure-temperature phase diagram.
• Whenever water is boiling or condensing, the system is somewhere on the boiling point line.
• Mouse hovers at: temperature = 0 °C, pressure = 0 kPa.
• ###### Draw the path taken by food during other techniques, such as brining and marinating, which involve parameters like acidity and salinity.
• Ice cream can partially explained by looking at a phase diagram for temperature and salinity, such as this one in The Physics of Ice Cream by D Goff (2003).

• ###### Calculate the energy needed to cause a phase transition is proportional to the mass of the food; the constant of proportionality is different for different materials.
• At the macroscopic level, the energy, U, needed to cause a phase transition is related to the mass, m, by a constant, L:

$$U = m L$$

• Some common values for latent heats of melting and vaporization are:
Material Heat of
melting (J/K)
Heat of
vaporization (J/K)
ethanol 108 846
nitrogen - 199
water 334 2257
• On a plot of temperature vs. heat added, these transitions correspond to horizontal parts on the plot.
• ###### Calculate, at the microscopic level, the energy, U, needed to cause a phase transition is equal to the energy needed to break apart the bonds between the molecules, which is proportional to the thermal energy, kBT, by a constant C. For water, C is about 3/2:

$$U = C k_B T$$

***

#### Texture: The way that food feels in your mouth, independent of its taste, can be explained in terms of the bonds holding the molecules together.

##### Mouthfeel is one of the most complicated subjects in food science, but we can start to quantify it with some simple measurements.

One of the most common measurements is to apply a force using a weight or other method, as shown below in the example from The Science of Good Cooking. The fat in the butter disrupts the protein network from the eggs, which makes it less elastic and unable to support much weight:

• ###### Draw simple diagrams and stress-strain graphs to describe the elasticity and fracture of a food.
• Based on Hooke’s Law, the elongation of a spring is proportional to the force applied, resulting in a linear plot of force vs. elongation.

$$k = \frac{F}{\Delta L}$$

where F is the force applied and ΔL is the elongation.

• Three-dimensional foods can be described in terms of stress (F/A) and strain (ΔL/L0):

$$E = \frac{F}{A}\frac{L_0}{\Delta L}$$

where E is the elasticity, A is the area over which the force is applied, and L0 is the initial size of the object.

For example, image that a piece of tofu is cm thick. When a force of N is applied over an area of cm2, then it depresses by mm. This implies that the the stress is Pa, the strain is , and the elasticity is Pa.

• ###### Calculate the elasticity of a material, based on physical measurements of its deformation.
• The stress of a material is equal to the force applied to a material, divided by the area.
• The strain of a material is a dimensionless way to describe the amount of deformation.
• The elasticity of a material is equal to the stress divided by the strain. Stiffer materials, which are more elastic, require more force for the same deformation.
• On a plot of stress vs. strain, stiffer materials have a stiffer slope; more stress is required to achieve the same deformation.
• ###### Calculate how the elasticity of a material scales with changes in the bonds at the microscopic level.
• The elasticity of a material is due to energy stored in the bonds between its molecules. More energy can be stored by increasing the density of bonds, or the energy stored in each bond. For a gel, the energy is roughly equal to thermal energy (kBT). The density of the bonds is equal to the reciprocal of the cross-link spacing, l, cubed:

$$E = \frac{k_B T}{l^3}$$

When l = nm and T = °C, then the elasticity is kPa.

• Small changes in the cross-link spacing can have major changes in the elasticity, as shown in the plot below:

• ###### Draw an approximation of how the microscopic structure of food changes when its elasticity changes.
• Extra firm tofu has a smaller cross-link spacing than silken tofu.
• Well-done steak has a smaller cross-link spacing that rare steak.
• The elasticity of a gel is inversely proportional to the density of cross-links.

$$E = \frac{k_B T}{l^3}$$

kB = 1.38 x 10-23 J/K (Boltzmann )

T = 300 K (Temperature)

When l = nm and T = °C, then the elasticity is kPa.

• ###### Give examples of how fracture is related to the properties of specific foods.
• (Yield stress/strain of pasta?)

***

#### Diffusion: The rate of many culinary processes, such as cooking and brining, is limited by diffusion, in which the distance travelled is proportional to the square root of time.

##### Timing is one of the essential aspects of good cooking, and the approximate times needed for different culinary techniques can be estimated based on the diffusion constant of water.
• ###### Draw the distribution of salt within a brined food, for different values of the diffusion constant
.

Below is a photo from The Science of Good Food, which shows how a blue dye penetrates to different depths in a potato, depending on the variety:

• ###### Draw the distribution of temperatures within a piece of food at different times during the cooking process.
• The temperature on the outer surface rises until it reaches the boiling point of water.
• Once the surface water has evaporated, the temperature can continue to rise.
• After another rise in temperature, browning reactions can occur.
• Meanwhile, heat diffuses inside and raises the temperature.
• Even after being removed from the heat, the temperature continues to gradually equalize.
• ###### Calculate the thickness of the cooked layer of a food, as a function of time, assuming no phase transitions in the food.
• The cooking times of most foods are limited by the diffusion constant, D, of water.
• The average distance, L, traveled by diffusing molecules (or heat), is related to the time, t, by:

$$L = \sqrt{D t}$$

• In theory, if the size of a food is doubled, then the cooking time increases by closer to a factor of four. Heat travels faster than other types of diffusion, so brining or soaking is often the most time-consuming step in a recipe:
• Below is a table of common diffusion constants, from
Mechaism Diffusion constant (m2/s
Heat (in water) 1.4x10-7
Heat (in food) 1.2 - 1.6x10-7
Water (in water) 1.7x10-9
Sucrose (in water) 4.7x10-10

from Physical Chemistry of Foods ed. by Pieter Walstra and The Practical Guide to Sous Vide Cooking by Douglas Baldwin

• ###### Calculate an approximate cooking time, given the size of a piece of food, as well as the starting and external temperatures.
• Foods cook faster if the external temperature is higher.
• The temperature rise is fastest at the start of cooking, then slows down as the temperature of the food approaches the final temperature.

***

#### Gelation: One way to change the texture of food is by adding polymers; at low concentrations these can thicken a liquid and at high concentrations they can link together to form a solid.

##### Many foods are solid, yet they are mostly made of water; how is this possible? Gelation is one way that a smaller number of long polymers can hold liquid water into a solid.
• ###### Give examples of common gelling agents:

Below is a photo of gels made with several different gelling agents:

##### Types of hydrocolloids (see Khymos):
Gelling agent Origin Mechanism
Agar seaweed heat
Gelatin animal heat
Gellan (low-acyl) microbes heat
Gellan (high-acyl) microbes heat
Methylcellulose microbes heat
Pectin (low methoxyl) plan heat
Pectin (high methoxyl) plant heat
Sodium alginate (low methoxyl) seaweed heat
Xanthan gum microbial **

** = with locust bean gum

• ###### Give examples of spherification, both normal and reverse.
• Normal spherification: alginate solution into calcium bath
• Reverse spherification: calcium solution into alginate bath
• ###### What's the diffusion constant of calcium ions in the shell, given the distance and the time?

If the shell thickness is mm after min, then the diffusion constant is cm2/s.

***

#### Flow: An important aspect of the consistency and mouthfeel of many liquid foods is how easily they flow.

##### The consistency of sauces and beverages can be quantified by their viscosity; additives are typically used to achieve the desired viscosity of a food.
• ###### Give examples of some thickening agents used by chefs, and the approximate percentages.
• Traditional thickening agents, like starch or pectin, require about 5% by weight.
• Modernist ingredients, like xanthan gum or carrageenan, require less than 1% by weight.
• ###### Draw different types of thickeners, to explain differences in their thickening power.
• Xanthan gum is longer than starch, so it is a more effective thickener.
• Amylopectin is branched, so for the same molecular weight it is less effective than amylose.
• ###### Calculate how the elasticity, E, of a material is related to its viscosity, η by a time constant, τ.

$$\eta = E \cdot \tau$$

***

#### Emulsions: Another way to change the texture of food is by adding droplets or bubbles; at low concentrations they can thicken a liquid and at high concentrations they can pack together to form a solid.

##### Understanding emlsions is crucial for achieving accuracy in the consistency of sauces or baked goods.
• ###### Give examples of emulsions or foams.
• Chefs often thicken sauces by incorporating oil droplets into an aqueous phase. This works because the oil is hydrophobic and doesn’t dissolve in water.
• Many pastries and some other foods are foams, since they contain numerous air bubbles.
• ###### Draw at least one way in which an emulsion or foam can fail, and where surfactants are used to stop this from happening.
• For a cook, failure means that the emulsion separates into its components. This process can be slowed down using various surfactants, as shown in this series of photos from The Science of Good Cooking:

• Coalescence: droplets combine into a single one.

• Ostwald ripening: the contents of smaller droplets enter a larger one, because of the pressure difference.

• Surfactants: coat the surfaces of the droplets or bubbles, to prevent coalescence.

• Polymers can hold the droplets or bubbles in place, making them less likely to coalesce.
• ###### Calculate the energy stored at the interfaces of all the drops in an emulsion.
• Compare this energy to the mechanical energy of mixing.
• ###### Calculate the elasticity of an emulsion, based on the relative amounts of the components.
• An emulsion becomes elastic once it exceeds a critical volume fraction.

• Emulsions (and foams) become solid when the concentration of bubbles, φ, exceeds the random close packing fraction, φc. The elastic modulus, E, depends on this volume fraction, as well as the surface tension, σ, and the droplets (bubble) size, R:

$$E = \frac{\sigma}{R} (\phi - \phi_c)$$

Suppose you are whipping an egg white solution with a kitchen mixer. Assume that the surface tension is mN/m and the bubble size is mm. If the volume increases from 200 mL to mL. In that case, the volume fraction is and the elasticity is Pa.

• The elasticity of the emulsion or foam is stronly affected by bubble size, as shown in the plot below:

• The droplets or bubbles are rarely the same size; a property called polydispersity.

***

#### Chemical reactions: the atoms in the basic molecules of food can rearrange to produce more flavorful compounds.

##### So far we have looked at transformations that rearrange the molecules within a food; however, to produce new flavors, the atoms themselves must be rearranged. Chemical reactions are also responsible for producing carbon dioxide gas for leavening.
• ###### Give examples of chemical leaveners used in baking:
• Baking soda reacts with an acid to produce carbon dioxide gas. For every mole of baking soda, one mole of carbon dioxide is produced. In the reaction below, baking soda (NAHCO3) combines with vinegar (CH3COOH):

$$NaHCO_3 (s) + CH_3COOH(l) \rightarrow CH_3COONa(s) + H_2O(l) + CO_2(g)$$

If there are g of baking soda in a recipe, then then volume of carbon dioxide gas produced is liters.

• Baking powder already contains an acid, so it produces carbon dioxide gas in the presence of water and heat.

$$NaHCO_3 (s) + C_3H_5O_4COOH(l) \rightarrow C_3H_5O_4COONa(s) + H_2O(l) + CO_2(g)$$

• Sometimes it is advantageous to use both baking soda and baking powder. This raises the pH of the batter, weakening the gluten, and improving the texture of the final cookie by allowing the dough to spread out more:

• ###### Give examples of browning reactions that produce new flavor molecules:
• Caramelization describes the set of reactions that occur when sugar molecules are heated above 165 °C, such as when preparing onions for paella.

• Maillard reactions occur between amino acids and carboyhdrate molecules. The reaction proceeds fast at higher temperatures, so it is typically observed at temperatures about 120 °C. This process can be sped up when cooking proteins by adding sugar, as shown below in the experiment from The Science of Good Cooking:

• Oxidation reactions occur between phenolic compounds and oxygen. These are accelerated by enzymes, which are often already present in the food. These enzymes can be deactivated by blanching, as shown in this experiment from The Science of Good Cooking:

***

#### Fermentation: microbes produce acid and other flavorful molecules as the digest the sugars in a food.

##### Many cooking techniques are designed to kill any potentially harmful microbes; fermented food promote beneficial bacteria, so that the dangerous ones are eliminated.
• ###### Give examples of fermented foods from around the world:
• Dairy: yogurt, cheese, kefir
• Vegetables: pickles, kimchi, sauerkraut, chocolate
• Beverages: beer, wine
• Suaces: fish sauce, soy sauce
• ###### Give examples of the role of yeast in leavening:

Yeast produce carbon dioxide through chemical reactions; this process happens slower at cooler temperatures. At higher temperatures, the reactions are faster, but the cells run out of food and die, as shown in The Science of Good Cooking:

• ###### Calculate the population of bacteria, assuming no contraints on their growth:

The number of bacteria as a function of time, N(t), depends on the starting population N0 and a time constant, k:

$$N(t) = N_0 e^{kt}$$

The time constant, k, is related to the doubling time τ by:

$$k = \frac{\ln(2)}{\tau}$$

From the graph below, you can see how after a few hours, for a doubling time of 20 minutes, the population increases in size by a factor of several thousand:

This is an early prototype developed by Naveen Sinha and is still under development. If you have any feedback, send him an e-mail.

This website was made possible thanks to the efforts of numerous people including: Prof. David Weitz, Prof. Michael Brenner, Prof. Amy Rowat, Prof. Otger Campas, Christina Andujar, Daniel Rosenberg, Ferran Adria, Pere Castelles, Héloïse Vilaseca, Harold McGee, John McGee, Pia Sörensen, Aileen Li, Jason Doo, Geoff Lukas, Johnny Siever, Eli Feldman, Lily Robles and Julia Frenkle-Kunelius, Dan Souza, Rolando Robledo, Phil Desenne and the PITF Program, and many others.