PY 107 – Physics of Food & Cooking
Homework 1
Homework 1 -- Food Components / Phase Transitions
Due Thursday, Feb. 20, 5pm in homework box near SCI 121
or by email (rb@bu.edu)
Collaboration Policy: You are allowed to collaborate with fellow students in this class
on this homework. Write-ups should be carried out individually by each student, with any
collaborators noted.
Theme:
The major components of food are polymers whose interactions both with themselves
and other molecules can be altered by changes in temperature and pH.
Molecular interactions determine the phase behavior of materials.
Phase transitions can be achieved by changing temperature, pressure, pH or adding
other components.
Learning objectives:
 Understand the major characteristics of the three essential components of food
(carbohydrates, proteins and fats).
 Food contains energy. The energy is stored in high energy molecular bonds that
are broken down when food is digested.
 The bonds that are broken down during digestion have much higher energy than
those that are manipulated when cooking.
 Kinetic Energy of molecular motion can be related to temperature.
 Temperature increases when a material is heated, decreases when cooled.
 Understand the concept of specific heat.
 Temperature remains constant while a substance is melting or freezing or boiling
or condensing. Understand what is latent heat.
 Understand what phase behavior is and learn how to read a phase diagram.
 Understand how chefs use phase diagrams to manipulate foods.
 Understand the connection between cooking induced phase changes and
molecular structure and molecular interaction energies.
 Understand the effect of pressure and solute concentration on phase transition
temperatures.
 Understand the idea of entropy and the increase in entropy by mixing.
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PY 107 – Physics of Food & Cooking
Homework 1
OVERVIEW
In this topic we introduced the relevant energy scale for different types of
interactions between atoms and molecules. We discussed food molecules
themselves. The table below summarizes the major points of discussion.
Interaction
Types of
interaction
Relevant
energy scale
How it relates to
cooking
Fatty acid chains
of a triglyceride
Van der Waals
interactions
2kJ/mol
Melting temperature
of fats
Secondary
protein structure
Hydrogen bonds,
electrostatic and
van der Waals
interactions
2-20kJ/mol
Eggs, enzyme activity
~330kJ/mol
Energy released in
digestion, food
texture, marinades
Monomers of a
Polymer
Covalent bonds
Equations:
1 Calorie =1000 calories
= 4.18 kJ
U = C kB T for energy of 1 bond

kB = 1.3806488×10−23 J/K
Avogadro’s Constant NA = 6.02214129×1023 mol−1
(this is the number of atoms or molecules in a gm mol of the
substance)
For the simplest approximation use C =3/2 (strictly valid for monatomic
atoms, but works quite well at low temperatures, ~ up to 200 K = -73 C. ) A
better approximation for diatomic molecules like CO or O2 or H2 is to use C
= 5/2 for the usual cooking temperatures 0 to 300 C, and C=7/2 for very high
temperatures, greater than 2000 K.
Heat, Q= mCp ΔT where ΔT = Tf - Ti , the difference between final and initial
temperatures and Cp is the specific heat of the substance, m its mass.
Heat needed to transform mass m of a material from solid to liquid or gas
while the temperature remains constant at the melting (freezing) or boiling
(condensation) temperature is given by
2 Q = mL where L is the relevant
latent heat.
PY 107 – Physics of Food & Cooking
Homework 1
Problems
(1) COVALENT BONDS: ENERGY
Our bodies break down the food that we eat to give us energy. The point of this
problem is to connect the caloric content of the food, as is written on food
containers, to the energy of the bonds. Food calorie content is often expressed
in terms of the 4-4-9 rule: Namely, carbohydrates, proteins, and fats contain 4
Cal/gram, 4 Cal/gram and 9 Cal/Gram, respectively. [Note that 1 kcal = 1000 cal
= 1 Cal --the dietary Calorie].
(a) One gram of olive oil has 8.8 Cal. The molecular weight of a typical olive oil
molecule is 885.5 g/mol. Compute the energy content of olive oil in kJ/mol.
Given the order of magnitude of the bond energies (covalent, van der Waals,
hydrogen bonds), what types of bonds are being broken and re-formed during
the digestion of olive oil?
(b) A single molecule in olive oil contains many types of covalent bonds, each
with different strengths. The bonds in a typical single molecule of olive oil are
as follows:
Reactants
C=C double
bond
C-C single
bond
C-H
bond
C=O double
bond
C-O single
bond
Number
3
50
104
3
6
Energy
610 kJ/mol
347
kJ/mol
413
kJ/mol
748 kJ/mol
358 kJ/mol
Digestion requires oxygen molecules to be broken down. The products of
digestion are CO2 and water (H2O):
C=O double O-H single
Products
bond
bond
O=O double
Reactants
bond
Number
114
104
Number
80
Energy
498 kJ/mol
Energy
803 kJ/mol
464 kJ/mol
Compute the total energy released by digestion of olive oil, by subtracting the
energy required to break up the reactants from the energy released by
forming the products. Compare your answer to that computed in (a).
(c) One serving of tofu (91 grams) contains 2 grams of carbohydrates, 9 grams of
proteins, and 5 grams of fats. Compute its energy content in Cal/gram.
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PY 107 – Physics of Food & Cooking
Homework 1
(2) Calories in Brownies:
(a) A food label for Brownies is shown below. Using the 4-4-9 rule discussed
in the lecture, calculate the energy content of a single brownie in units of (i)
Calories , (ii) Joules.
(b) If you walk at a constant speed up a hill with a slope of 30 degrees to the
horizontal how much distance would you need to walk uphill to use up all the
calories from the brownie. Ignore the calorie consumption to maintain your
basal metabolic rate.
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PY 107 – Physics of Food & Cooking
Homework 1
(3) PHASE CHANGES, MOLECULAR STRUCTURE AND COOKING: Lipids
The basic ideas we discussed with phase behavior of water and simple materials
also are relevant to cooking materials. Here we apply this to the melting behavior
of fats.
(a) By looking up on the internet, make a phase diagram showing the solid to
liquid transition of olive oil and coconut oil, i.e. on the line below indicate by
an arrow the melting temperature of the oil, and label the two regions by their
phase : LIQUID or SOLID.
OLIVE OIL
COCONUT OIL
(b) Convert the melting temperature from ° C (Celsius) to ° F (Fahrenheit).
(c) Olive oil contains ~75% unsaturated fatty acids; and coconut oil contains
>90% saturated. Discuss your observations of the observed melting
transition temperatures with respect to the molecular composition of these
oils. [Hint: Recall the class discussion of the different interaction energies of
saturated and unsaturated fats.]
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PY 107 – Physics of Food & Cooking
Homework 1
(4) BOILING A LIQUID
Look up the boiling points, and latent heat of vaporization of olive oil and liquid
nitrogen (online, or maybe in the lecture slides). Remember to always cite where
your values come from, so that if they are wrong, we can figure it out.
(i). Using the equation U = CkB T, and assuming that C = 1.5 for both, calculate
their interaction energies when they boil. NA and kB are fundamental constants.
(ii) Which one, olive oil or liquid N2 will cause a greater burn to your hand if you
dip it in? Explain why.
(iii) Using the same heater, same pot and same mass of oil or water, which heats
faster from room temperature to 80°C, oil or water? Explain why.
(iii). The strength of an average covalent bond is around 80 kcal/mol (1 kcal =
1000 cal, and 1 cal = 4.18 joules). Convert this energy into joules per molecule.
Using the equations calculate the temperature required to break a covalent bond.
What does this tell us about the kinds of bonds that are normally broken during
boiling.
(iv). As discussed in class boiling water involves breaking hydrogen bonds (Hbonds). Assuming that 90% of H-bonds are broken in boiling water estimate the
latent heat of vaporization in kJ/kg using on average 4 H-bonds per water
molecule, energy of H-bond = 20 kJ/mol of H bonds. Is this reasonable
compared to the value in textbooks or online.
(v). You are on a winter hike and run out of water in your cabin. There are plenty
of icicles hanging from the roof of your cabin. Assuming that the temperature of
the ice is -5 °C calculate how long will it take using a 500 W electric kettle to melt
250 g of ice and heat it to 175 °F to make some green tea (green tea is best
brewed at 175 °F.) Assume that 90% of the energy delivered by the kettle goes
into heating its contents.
Notes:
Specific heats. Cp ice = 2030 J/ J/(Kg °C), Cp water = 4180 J/(Kg °C).
Power in Watts = Energy (J)/ Time(s).
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PY 107 – Physics of Food & Cooking
Homework 1
(5) PRESSURE DEPENDENCE OF BOILING POINT
Here is the phase diagram for water:
(i)
(ii)
Does it take less time or more time to cook potato or custard or other
food in the pressure cooker than a conventional steamer. Use the
phase diagram to rationalize this difference.
After graduating from BU and successfully completing this course on
Physics of Cooking, you land an important position as the Chief
Scientist at Char-Broil, manufacturers of gas grills. Their website
http://www.charbroil.com/cooking-guides/cooking-chart-gas-grills.html
gives the following chart for cooking steak and hamburger.
FOOD
SETTING
COOKING TIME
BEEF
Hamburger ½" thick
Medium
Med: 7-10 min.
Steak ½"
Medium-Hot
Well done: 10-15 min.
Rare: 3-6 min.
Med: 6-9 min.
Well done: 9-12 min.
(iii)
Your new employer is interested in marketing their product to miners,
who work and cook at the bottom of mines, where the absolute
pressure is 1.5 atm. Explain qualitatively, using the phase diagram, the
cooking instructions for making hamburger at the bottom of a mine.
If the client was a ski resort at Vale, Colorado, altitude 2500 m what
would be the instructions you would provide for cooking time for the
hamburger. Ignore humidity changes with altitude which will affect the
surface temperature and evaporation rate, and assume that the
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PY 107 – Physics of Food & Cooking
Homework 1
temperature is the same everywhere. The focus here is on the cooking
time to get to the desired core temperature.
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PY 107 – Physics of Food & Cooking
Homework 1
(6) Cooking with Liquid Nitrogen
In the lecture you saw a demo of cooking marshmallows with liquid nitrogen.
(i) Assuming that a marshmallow is 20 ml in volume and its density is 0.37 g/ml
calculate its mass.
(ii) Would a lump of sugar of the same mass as the marshmallow be bigger or
smaller than the marshmallow in volume? Explain.
(iii) What temperature does the marshmallow reach after we let it sit in the liquid
nitrogen for a couple of minutes?
(iv) If the specific heat of marshmallows is 2 J/(g °C) how much heat is given off
when the marshmallow cools from room temperature (25 °C) to the temperature
of the liquid Nitrogen bath.
(v) Now you take the marshmallow out of the liquid Nitrogen bath and put it in
your mouth at 37°C. How much heat is removed from your mouth?
(vi) Where does this energy to heat up the marshmallow come from?
_____ The air in the room
_____ Your mouth
_____ Your stomach
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