Name:
TF Name:
Science and Cooking: Problem Set 7
Due on Canvas by 11 PM on Thursday, October 30th
Please type or write your answers within this document or on a separate sheet of paper.
Then save your work as either a Microsoft word document (.doc or .docx) or as a PDF
file (.pdf) and upload to Canvas. If you write your answers by hand, you may scan your
work and paste the images into either of these file types, but submissions that are NOT
either of these file types will not upload properly. Your work must be organized and
legible – if your TF can’t understand what you wrote, they won’t give you credit.
Show your work for derivations and calculations. YOU WILL NOT RECEIVE FULL
CREDIT WITHOUT SHOWING YOUR WORK. Be sure to calculate all results fully
(don’t leave numbers in fraction form, or in terms of pi, etc) and to provide answers in
the requested units, if applicable.
Equations of the Week
𝜑=
Concept
φ
Vdispersed
Vtotal
𝑉𝑑𝑖𝑠𝑝𝑒𝑟𝑠𝑒𝑑
𝑉𝑡𝑜𝑡𝑎𝑙
Description
Volume fraction
Volume of dispersed phase (particles and droplets)
Total volume of the mixture
Units
Unitless
L
L
Name:
TF Name:
Question 1: Lab Follow-up (18 points)
In lab this week, you made four different Mac and Cheese recipes, and measured the
viscosity of the sauces by seeing how quickly they flowed through macaroni noodles. The
recipes are copied below. Three of these recipes contained flour which is made up of 75%
starch by weight: The density of flour is 0.59g/mL. A typical starch granule swells to 30x its
original volume during hydration.
Sauce A
Sauce B
(no flour)
Sauce C*
(no milk)
Sauce D
(no cheese)
1tbsp butter
1tbsp butter
1tbsp butter
1tbsp butter
1/2 tsp flour
-
1/2 tsp flour
1/2 tsp flour
1/2 cup milk
1/2 cup milk
-
1/2 cup milk
1/4 cup (58 g)
American cheese
1/4 cup (58 g)
American cheese
1/4 cup (58 g)
American cheese
-
1/4 cup (58 g)
Velveeta cheese
1/4 cup (58 g)
Velveeta cheese
1/4 cup (58 g)
Velveeta cheese
-
a. What is the volume fraction of cheese in the finished cheese sauce A? (3 points)
φ = Vcheese/Vtotal
Vcheese = 0.5C
Vflour final = Vhydrated starch + Vrest of flour
Vhydrated starch = 0.75 · 0.01042Cflour · 30 = 0.23C
Vflour final = .23C + (0.25 · 0.01042C) = 0.23C
Vtotal = 0.5C cheese + 0.5C milk + 0.0625C butter + 0.01042C flour = 1.07C
φ = 0.5/1.07 = 0.47
b. What is the volume fraction of hydrated starch granules in the finished cheese sauce
A (3 points)
from part a: Vhydrated starch = 0.23C
φ = Vhydrated starch/Vtotal
φ = .23/1.07 = 0.21
Name:
TF Name:
c. What is the volume fraction of hydrated starch granules in the finished cheese sauce
D? (3 points)
from parts a and b, hydrated starch volume and flour volume is the same
Vtotal = 0.5C milk + .0625C butter + 0.01042C flour = 0.573C
φ = Vhydrated starch/Vtotal
φ = .23/0.573 = 0.4
d. For parts a, b, and c, is this volume fraction high enough to contribute significantly to
the sauce’s viscosity? (6 points)
for part a, no because it’s less than 0.5, but it is close!
for part b, no because it’s less than 0.5
for part c, no because it’s less than 0.5, but it is close!
the ingredients must have to work together to increase the viscosity of the sauce
e. Which ingredient is more important for the viscosity of the final sauce? Explain. (4
points)
For sauce A, cheese seems to be more important, but the flour and cheese likely
work together to make the sauce viscous
For sauce D, flour is the most important. There is no cheese.
Question 2: Martin Breslin’s Coq Au Vin (17 points)
We have mostly talked about the use of carbohydrates as thickeners, but other major food
components can function as thickening agents as well. This week, Martin Breslin made Coq
Au Vin in class which he thickened using rooster blood!
a. Blood is primarily composed of a little over 54% plasma, 45% red blood cells and
less than 1 percent white blood cells. Plasma is 92% water and 8 % plasma proteins.
What is the total volume fraction of the components of blood that contribute to its
viscosity? (3 points)
φ = (Vcells + Vproteins in plasma) /Vtotal
Vtotal = 100
Vcells = 45 + 1 = 46
Vproteins = 54 * .08 = 4.32
φ = (46 + 4.32)/100 = 0.50
Name:
TF Name:
b. Now let’s imagine that you heat the blood. When you do this, the different
components of the blood can change. Hypothesize what these changes might be
and explain in a few sentences how they might change the volume fraction of the
blood. Design an experiment to test your hypothesis. Make sure you note your
hypothesis, what your controls in this experiment are, what you are measuring and
how you are measuring it, and what you expect to find. (14 points)
Question 3: Xanthan Gum White Sauce (42 points)
If you are confused by these calculations, it may help to watch the supplementary video on
Modernist Thickeners
(http://cm.dce.harvard.edu/cs50player/youtube.html?title=&youtube_id=ThPZIu219nw&srt_
url=srts/ThPZIu219nw.srt) (Note: There is a mistake in this video at 2:28 in the equation
for polymer radius. Please use the equation taught in lecture).
..
a. In class, you saw a demonstration of how to thicken a white sauce in two ways, but
there are actually four ways to thicken a sauce. What are they? (4 points)
adding starches, adding fats to make emulsion, adding modernist thickener,
reduction
b.
Describe how the viscosity changes in terms of the equation of the week for the four
methods above. (8 points)
adding starches: when you add starch granules, they absorb water and swell,
increasing their volume. As the volume of the particles increases, the volume fraction
they take up increases, the viscosity increases
adding fats: when you add oil, it can form an emulsion (oil droplets in water). These
droplets increase the volume fraction f the particulate matter in solution, increasing
the viscosity
adding a modernist thickener: when in solution, these polymers can stretch out and
move around via the random walk which gives them a very high volume fraction,
increasing the viscosity of the solution
reduction: In a reduction, you reduce the volume of the liquid the particles are
dissolved in while the volume the particles take up stays the same. This increases
the volume fraction of the particles and the viscosity
c. You need a very small weight percent of xanthan gum to increase the viscosity of a
sauce. What properties of xanthan gum make it such a good thickener? (3 points)
long polymer – in solution, this gives it a large hydration radius as it wiggles around
via the random walk.
Also, it has very little taste, and dissolves well in water
Name:
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d. The polymers in xanthan gum are made up of sugar monomers with the molecular
formula of C35H49O29. What is the molecular weight of the xanthan gum monomer? (3
points)
1pt for knowing how to calculate this
1pt for correct MWs
35 · 12g/mol C + 49 · 1g/mol H + 29 · 16g/mol O = 933g/mol
e. The average xanthan gum polymer is made up of about 10,000 monomers. What is
the molecular weight of the polymer? (3 points)
MW polymer = MWmonomer · Number monomers
MW polymer = 933g/mol · 10,000 monomers = 9,330,000g/mol
f.
If the radius of xanthan gum monomer is 0.4nm, what is the radius of the polymer?
(3 points)
rpolymer = √(N)·r
rpolymer = √(10,000)·(0.4nm) = 40nm
g. If the sauce contained 2% xanthan gum by weight, and you have 1L of sauce, how
many molecules of xanthan gum polymer does your solution contain? (4 points)
1L · 1kg/L = 1kg sauce
1kg · 0.02 = 0.02kg or 20g xanthum gum
20g · 1mol/9,330,000g = 0.00000214mol
0.00000214mol · 6.022·1023molecules/mol = 1.29·1018molecules
h. What is the volume of each xanthan gum polymer? (3 points)
V = 4/3πr3
V = (4/3)π(40nm)3 = 268,082nm3
also acceptable to assume it spreads out as a cube
V = r^3
V = = 64,000nm3
i.
Calculate the volume fraction of xanthan gum in your sauce (3 points)
Answer from part g
φ = (Vxanthan) /Vsauce
Vxanthan = 1.29·1018molecules · 268,082nm3 = 3.46·1023nm3 = 346cm3
Name:
TF Name:
φ = 346cm3/1000cm3 = 0.346
j.
These thickeners might seem pretty unusual, but xanthan gum is actually a very
common food additive (especially in salad dressings, sauces, and ice creams).
Please name one food you ate this week that had xanthan gum in it or that you think
might have had xanthan gum in it. How would the food been different without
xanthan gum? (4 points)
k. What are some other thickening agents that aren’t mentioned in this problem set?
List at least two (2 points).
Question 4: Bill Yosses’s Candy Apple (13 points)
Viscosity can change so much that it can take something from a liquid to a solid. To see a
demonstration of this, please watch Chef Bill Yosses’s video on making an apple out of
sugar
glass
(http://cm.dce.harvard.edu/cs50player/youtube.html?title=&youtube_id=1YtF_uAvTQA&srt_
url=srts/1YtF_uAvTQA.srt).
a. While being heated, the sugar water mixture was a liquid, and Bill Yosses was
unable to manipulate it. But, later on, he was able to stretch it and shape it into any
shape. What variable did Bill Yosses control to allow for this change? (3 points)
He manipulated the temperature
b. Bill Yosses mentioned at one point that it is important only to put the sugar glass ball
down on the counter top very briefly. What happens when you set it down for a long
time? Why is it important not to do this for a successful candy apple? (5 points)
When he sets it down, the heat quickly escapes in to the cold counter top
When the temperature decreases, the viscosity in that area increases relative to the
rest of the sugar.
Then, when you try to blow the apple, the parts with an increased viscosity won’t be
able to stretch while the parts with a low viscosity will, resulting in a misshapen apple
You were so inspired by Bill Yosses’s candy apple that you decide to make something
with sugar glass. For a Halloween treat, you decide to make broken glass cupcakes like
the
one
below
(recipe:
http://allrecipes.com/recipe/bloody-broken-glasscupcakes/Detail.aspx).
Name:
TF Name:
c. However, when reading the reviews, you find one person who is angry because their
sugar glass ended up chewy and sticky. What is one thing they could have done
wrong? (3 points)
If the glass is chewy, it is less viscous than the sugar glass.
Likely, they didn’t evaporate enough water (volume fraction of sugar is too low)
d. Another common problem people seem to have with this recipe is that they can not
get the blood to stick to the sugar glass because its viscosity is too low, and it just
drips off, leaving a puddle on top of the cupcake. How could they solve this problem?
(3 points)
If they want it to stick, they should increase the viscosity of the blood.
They could add more sugar or xanthan gum or starch or reduce it or add oil maybe
(gross)?
Question 5: Final Project Ideas (10 points)
In his talk, Ferran talked about the many “W” questions (i.e. Why, What, When, How,
Where, etc) that can be used to explore creative culinary questions. Please write down 5
culinary questions each starting with one of these “W” words that you have wondered about
and would like to explore further. This is a good way for you to think broadly about topics for
your final project, and will form the basis for discussions with the course staff about how to
design the project. You will not be obligated to pick one of these in the end. If you’re having
trouble, google a recipe you’re interested in, and for each step, try and think of questions
like the ones below.
Example Questions:

Why do you mix the butter and sugar first when baking cookies?
Name:



TF Name:
Would it be possible to make a pie crust in to a foam?
What determines the texture of roast chicken?
How can you predict the length of time you need to let bread rise?