SCIENCE AND COOKING FROM HAUTE CUISINE TO SOFT MATTER SCIENCE FINAL EXAM FALL 2012 PRACTICE FINAL EXAM 2013
Problems in red cover material that has not been covered
this year and can be ignored
NAME: ______KEY___________ SECTION TIME:_____KEY______ Please write your name on every page. True/False questions require no explanation. Show your work for all other questions. APPETIZER MAIN COURSE DESSERT TOTAL /50 /70 /45 /165 2
Unit conversions N = kg∙m/s2 J = N∙m Pa = N/m2 = J/m3 1 L= 1∙10‐3m3 1 ml = 1 cm3 Kelvin = Celsius+273 Fahrenheit = (Celsius*9/5)+32 Area circle = r2 Volume sphere = 4/3r3 Surface area sphere = 4r2 Constants Room temp = 23˚C 1Cal = 1000 cal = 4.18 kJ Specific heat water 4.19 J/gK Boltzmann constant (1.38∙10‐23 J/K) Gravitational acceleration (g=10 m/s2) Avogadro’s number (6.022∙1023 molecules/mol) Dheat water 1.410‐3 cm2/sec DCa 8.010‐10 m2/sec Equation pH  log[H  ] U  CkB T E
F /A
L / L0
E
kB T
l3
L  4Dt
T(t)  (Tinitial  Texternal )e (t /  )  Texternal
R2
where  
4D
Description Units [H+] Concentration of hydrogen ions Q Heat J m Mass g cp Specific heat J/gK or J/g˚C ∆T Change in temperature K or ˚C U C
kB
T
E
F
A
∆L
L0
E
kB
T
l
t
L
D
T(t)
Tinitial
Texternal

R
D
3
Bond energy for liquid to gas transitions Constant (1.5 for water) Boltzmann constant Temperature
Elastic modulus
Force
Area over which force is applied Change in length
Initial length
Elastic modulus
Boltzmann constant
Temperature
Cross‐linking spacing
Time to diffuse
Distance of diffusion
Diffusion coefficient
Temperature at cooking time t Initial temperature of food Temperature of surroundings Time constant
Shortest distance to center of food Diffusion constant of heat mol/L J ‐‐
J/K
K
Pa N
m2
m
m
Pa J/K
K
m
s
m
m2/s
˚C
˚C
˚C
sec
m
m2/sec
Equation 
  E 
E

E
E

R

(  C )
  C
NaHCO3 + AcidH  AcidNa + H2O + CO2
N(t)  N 0 e kt
where k 

C R
ln 2

NaHCO3
AcidH
H2O
CO2
N
N0
k
t

4
Description Units
Viscosity
Elastic modulus
Time constant
Elastic modulus
Surface tension
Radius of bubbles
Volume fraction
Critical volume fraction for onset of elasticity Sodium bicarbonate, baking soda Any acid, such as tartaric acid Water
Carbon dioxide
Population at time t
Initial population
Population growth rate Time
Doubling time
Pa∙s
Pa
s
Pa N/m
m
–
0.64
‐
‐
1/s
s
s
Appe
etizer [10 questions,, 52 pointss total] ` 1. [3
3 pts] True o
or False. Xanthan gum haas a calorie ccontent of 99 cal/g. FALSSE 2. [5
5 pts] A stick of butter weighs 110 grams. How
w much eneergy must bee supplied tto raaise the buttter to its melting m
poin
nt (34˚C), staarting from a room tem
mperature o
of 23˚C. The spe
ecific heat off butter is 1.26 J/g˚C. Q=mcpdeltaT Q=110g * 1
1.26 J/g˚C * 1
11˚C = 1500 J 3. [3
3 pts] Which
h has a large
er mesh size
e: 4% by weeight agar aggar gel, or 1
1% by weigh
ht aggar agar gel?? Briefly exp
plain. 1% gel. more cross‐links can forrm between strands. It’ss the distancce The more agaar agar the m
oss‐links that determine
e the mesh size. So th
he fewer crross‐links th
he between cro
onger/largerr the mesh siize. lo
Or: O A gel witth 4% agar agar a
has a higher h
elastic modulus ((we know th
his intuitively frrom lab etc). A higher E means a sm
maller l according to thee equation EE‐kT/l3. So th
he ge
el with little agar agar m
must have a llarger l. 4. [3
3 pts] You drop two diffferent balls through a ccylinder with
h goo to try to figure ou
ut th
he viscosity of the goo. TThe first ball has a radiuus of 2R, the other has a radius of 5R
R, and both havve the same density. Doe
es the largerr ball have a higher or lo
ower terminaal ve
elocity? The larger b
ball, 5R 5. [5
5 pts] The elasticity e
of a substance is 3x1010 Pa and thee relaxation time 1x10‐12 se
econds. Whaat is the visccosity? viscosity = EE * tau = (3xx1010 Pa) * (1
1x10‐12 s) = 0 .03 Pa*sec
5 pts] In laab we made
e non‐melt,, low‐fat m
milkshakes using xanthaan gum as a 6. [5
th
hickener. Drraw two pictures of what w
the fluuid particless and the xxanthan gum
m polymers look like on a m
molecular levvel at the higghest and lo
owest concentrations yo
ou used. Blue do
ots are fluid particles, bllack lines aree xanthan gu
um polymerrs HIGHEST CONCENTRA
ATION LLOWEST CONCENTRATIO
ON 5
7. [5
5 pts] The re
ecipe below describes how to makee pretzels. N
Name the inggredients an
nd th
he processess that cause the pretzelss to be brow
wn and briefly explain wh
hy. 1. Maillard rreactions between the sugars (from brown sugaar and flour) and the proteins ((primarily fro
om flour) wh
hen heated aaccount for most of the browning.
2. Caramelizzation betwe
een the sugaars when heaated is also possible. 3. The bakin
ng soda raise
es the pH, prromoting Maaillard reactiions. 6
8. Below is a re
ecipe for making Southe
ern Sweet Teea and a graaph showingg solubility o
of su
ucrose as a ffunction of ttemperature
e. a. [5 pts] Givven that 1 ccup of waterr is 240 ml aand 1 cup off sugar is 20
00 g of sugar, calculate the sugar raatio (g sugarr/g water) att Step 5. Wo
ould the sam
me amount o
of sugar disssolve in wate
er, if the water was at rooom temperrature insteaad of boilingg? Explain ussing the grap
ph below. Ratio: 400
0/480 = 0.83
3 g sugar/g w
water From the solubility diagram, the ssolubility lim
mit is 4.8 g/g at 100˚C, an
nd 2 g/g at 20˚C, so in
n theory, you could dissolve all the ssugar in Step
p 5 both at b
boiling temp
p and room
m temp. (At b
boiling temp it would disssolve fasterr though) 7
b. [5 pts] What is the caalorie conten
nt of a 300 ggram servingg of Southerrn Sweet Iceed e your answe
er in units off Cal. Tea? Give
400g sugaar total = (40
00g)* (4Cal/gg) = 1600 Caal about 8 cups of water total = (8cu
ups)* (240 m
ml/cup) = 1920 ml = 1920 grams This also iincludes 2* 200 g sugar = 400 g So total m
mass = 1920 + 400 = 2320 g So Cal con
ntent is 1600
0 Cal/2320 gg = 0.69 Cal//g So in 300 g there are (0.69 Cal/g) * (300 g) = 2206 Cal 9. [5 pts] In the recipe for hard can
ndy below, it says to heeat the wateer mixture tto “300 to 310 degrees FF”. Why is th
his possible?? Most of the water has boiled off by the time the mixturee reaches 300 degrees Fahrenhe
eit. The concentration off the sugar iss therefore vvery high, wh
hich has significantly elevated the boiling point for thee remaining water. 8
10. [6 pts] Be
elow are the ingredients for Joanne Chang’s yelllow birthdayy cake. Briefly explain all of the diffferent mech
hanisms tha t contributee to the flufffiness of th
he cake, i.e. addition of aair into the b
batter. (1 se ntence/mecchanism). Ingredients for Yellow Birtthday Cake 1. Baking powder: contains sodium bicarbonaate/baking ssoda and tarrtaric acid that reactt to produce
e carbon dioxxide gas, whhich contribu
utes to fluffin
ness. 2. Baking soda and bu
uttermilk: so
odium bicarbbonate reactts w/ acid in buttermilk to make ccarbon dioxide gas, as ab
bove 3. The suggar and buttter are cream
med, creatin g air pocketts in the buttter that contribute to fluffinesss. 4. The pro
oteins in the
e egg whites will help hoold air when whipped. 5. The leccithin from th
he egg yolkss will help staabilize air bu
ubbles in thee batter. 6. The salt will weake
en the gluten
n network m
made by the fflour, reduciing elasticityy wing the air b
bubbles in th
he cake to exxpand more in the oven. and allow
7. The cakke flour has low gluten ccontent, whiich results in
n a weaker ggluten network ((see above). 9
Main Course 11. Wine grapes typically have a sugar content of 20% by volume when harvested off the vine1, most of which is available as glucose. A dry red wine is fermented until all of the sugar has been converted to alcohol and carbon dioxide by the yeast, as illustrated in the balanced reaction below. C6H12O6  2CH3CH2OH + 2CO2 glucose ethanol carbon dioxide a. [5 pts] A typical wine bottle contains 750 ml of wine and is produced starting with the same volume of grape juice. What do you expect the final alcohol content of the wine will be? The molecular weight of glucose is 180g/mol. Ethanol has a molecular weight of 46 g/mol and a density of 0.7 g/ml. Give your answer in percent by volume. 750mL = 750g 20 % of that is sugar, i.e. (0.2)(750g) = 150g Moles of sugar: 150g * (1mol/180g) = 0.8mol Moles of ethanol: 2 * 0.8 mol = 1.6 mol Mass of ethanol: 1.6mol * (46g/mol) = 73g Volume of ethanol: 73g * (1mL/0.7g) = 104mL Ethanol percent by volume: 104mL / 750 mL = 13.8% alcohol b. [5 pts] Name three things you could do to make the wine taste sweeter. Briefly explain your reasoning. Stop the fermentation before all sugar has fermented Add sweet grape juice Use dried grapes Use frozen grapes Use “noble rot” grapes, i.e. grapes that have been infested with a fungus Add distilled spirit to the wine 1
McGee, On Food and Cooking, p. 725.
10
c. [5 pts] If the cork leaks, oxygen can get into the bottle and a different reaction will take place that spoils the wine. The reaction is shown below. How many grams of vinegar will be produced if all of the alcohol from (a) reacts? The molecular weight of vinegar is 60 g/mol. CH3CH2OH + O2  CH3COOH + H2O ethanol oxygen vinegar (acetic acid) Moles of ethanol from the reaction is 1.6 moles Therefore: Moles of vinegar from the reaction: 1.6 mol vinegar Mass of vinegar: 1.6mol * (60g/mol) = 96g 11
12. You were so inspired by the mayonnaise lab that you rushed home to try it on your own and measure the viscosity for fun! You start with one 20 mL egg yolk and 15 mL of vinegar. After incorporating 35 mL of olive oil, you get impatient and decide to predict the elasticity right away! a. [3 pts] What is the volume fraction of oil, assuming that the egg yolk is largely water? Volume Fraction = (volume of oil) / (total volume) = (volume of oil) / (volume of oil+ volume of egg +volume of vinegar) = 35/(35 ml + 20 ml + 15 ml) = 0.5 50% b. [5 pts] If the surface tension of the drops in the mayonnaise is 10 mN/m and you estimate an average radius of 0.05 mm with the help of a microscope, what would you predict for the elasticity, using the equation of the week and your answer in (a)? Why? 0: the equation of the week is only valid for volume fractions greater than the critical volume fraction (0.64) c. [5 pts] You continue adding oil until the mayonnaise is springier and you have added a total of 105mL of oil. What is the volume fraction of oil now? (volume of oil) / (volume of oil+ volume of egg +volume of vinegar) = 105/(105 ml + 20 ml + 15 ml) = 0.75 = 75% d. [5 pts] Using the same estimates for surface tension and radius from (b), and your answer from (c), what is the elasticity of the mayonnaise? 10
5
10
0.11
10
5
22 0.75
0.64 12
e. [5 pts] How many droplets of oil are there in the mayonnaise? 5 10
4
4
5 10
5.2 10
3
3
105
105
105 10
5.2 10
5.2 10
5.2 10
2 10 f. [6 pts] If the “head” of each phospholipid molecule in the egg yolk (i.e. the part of the molecule that would project from the surface of the oil droplets and protect it from the water phase) has an area of (10 Ångstroms) x (10 Ångstroms), how many phospholipid molecules do you need to cover the entire surface area of the oil droplets? (1 Ångstrom = 10‐10 m) Find total surface area of the droplets Surface area of 1 drop 4
4 5 10
300 10
3 10
Surface area of all drops # = 2 10
3 10
6 10
100 10
6
# 10
6 10 g. [6 pts] If the molecular weight of the phospholipids is 825 g/mol, how many grams do you need to emulsify the mayonnaise? How does this compare to the weight of the eggs added in the recipe if you assume that egg yolk has the same density as water (1g/ml)? 1
#
6 10
1 10
6.022 10
825
1 10
0.008
8 We added 20mL of egg yolks and assuming that the density is roughly that of water, we added about 20g of yolk. 8mg is way less than this. 13
14
13. In this recipe for Irish soda breaad, one tabllespoon of b
baking powd
der is added
d. The chem
mical reactiion that occcurs is de scribed bellow. Knowing that on
ne tablespoo
on of bakingg powder we
eighs 13.8g, that the mo
olecular weight of bakin
ng soda is 84
4 g/mol, the
e molecular weight of taartaric acid is 150 g/mo
ol, and that 1 mol of gas has a volum
me of 22.4 LL, answer thee questions below. NaaHCO3 + AcidH  AcidN
Na + H2O + CO
C 2
a. [5 pts] How manyy moles of so
odium bicarbbonate are in
n one tablesspoon of bakingg powder? Bakingg powder sh
hould have sodium bicarrbonate and tartaric acid
d at equal molarrities. This m
means that there are 13..8g / (84 + 1550 g/mol) = 0.059 moless of each in one taablespoon of baking pow
wder. Or: mass
MW 
moles
13.8  y
y
84g / mol 
150g / mol 
x
x
m of tartarric acid
y  mass
x  moles
m
of tartaaric acid or baking
b
soda
solve for x and y 
y  8.8g
x  0..06moles
b. [3 ptss] How man
ny moles of f tartaric ac id are in on
ne tablespoon of bakin
ng powder? Same as in (a) 15
c. [3 pts] How many moles of CO2 are produced from 1 tablespoon of baking powder. One molecule of carbon dioxide is produced per molecule of sodium bicarbonate, so 0.059 moles of CO2 are produced d. [4 pts] What is the maximum volume by which the bread can rise due to the baking powder? Do you expect it to rise this much? Why or why not? 0.06 moles * 22.4 L = 1.3 L We do not expect it to raise this much because some of the gas escapes and is not contributing to the volume of the bread. e. [5 pts] If you run out of buttermilk and instead substitute regular milk, what chemical reactions in the recipe will be affected. Buttermilk is acidic so it can react with the baking soda in the recipe (which is added in addition to baking powder) and thus contributes to the fluffiness of the cake. If you substitute regular milk the cake may not rise as much. 16
Dessert 14. The bacterium Clostridium botulinum grows in moist, oxygen‐free environments (notably, inside cans of fruits and vegetables) and produces a paralyzing toxin. The USDA recommends heat‐treating newly‐canned fruits and vegetables at 121°C in a pressure‐cooker for three minutes to kill C. botulinum that might have gotten inside. a. [5 pts] If the number of living C. botulinum decreases by half for every four seconds of cooking at this temperature, how much reduction is there after 3 minutes? t= 3 min = 180 sec tau = 4 seconds 2(t/tau) 2(180 seconds/4 seconds) = 3.5 x 1013‐fold reduction Or: N(t)/N0=ekt kt=(ln2/tau)*t =(ln2/4)*180 = 31.2 so N(t)/N0=e31.2 = 3.5 x 1013 ‐fold reduction b. [5 pts] Suppose that a can of particularly gnarly peaches contains one gram of C. botulinum at room temperature. If each bacterium weighs 1 picogram (10‐12 g), how many bacteria do you expect to find alive after the heat treatment? 1 gram * (1 bacterium/10‐12 g) = 1012 bacteria to start with, i.e. With a 3.5 x 1013 ‐fold reduction,  bacteria remaining = 1012/(3.5 x 1013) = 0.03, i.e 0 bacteria remaining 17
c. [5 pts] A 200‐gram can of peaches winds up with a single C. botulinum cell. If the bacteria grow exponentially, dividing once every 50 minutes, how long would it theoretically take for the mass of the bacteria to exceed the initial mass of the peaches assuming there is unlimited nutrients and space for them to grow in? Need to find when there are 200 grams of bacteria 200 grams * (1 bacterium/10‐12 g) = 2 x 1014 bacteria i.e. N(t) = 2 x 1014 bacteria tau = 50 min N0=1 t = ? plugging into the equation: Or: N(t) = N0ekt 2 x 1014 = 1 * e^((ln2)t)/50 minutes)  t = 2375 minutes or 40 hrs d. [3 pts] Like baker’s yeast, C. botulinum grows by fermentation. Explain why this causes the characteristic bulging of metal cans containing food contaminated with C. botulinum. One product of fermentation is carbon dioxide gas. As more gas is produced, the pressure in the can will increase, ultimately causing the can to deform. 18
15. Dulce de leche is a sauce made by heating sweetened condensed milk until it turns brown and thick. It can be prepared by placing a sealed metal can of sweetened condensed milk in a pressure cooker, submerging it in water, and bringing the pressure cooker to a boil at 121°C for 15 minutes. a. [5 pts] Name two processes that might contribute to the brown color of the final product. Given the chemical composition of the ingredients, how would they cause browning in dulce de leche? Caramelization and Maillard reactions can both contribute to browning. Milk contains both sugar and protein so both can happen (i.e. both sugars and amino acids are present). b. [5 pts] Explain how the pressure cooker works in 3 sentences or less. How does this cooking method allow the contents of the can to reach the necessary temperature for browning? When the pressure cooker is placed on the burner, the water heats up to 100 degrees and begins to boil. This releases steam, which remains trapped inside of the pressure cooker, causing the pressure to rise. The boiling point of the water is elevated by the increasing pressure, so the water heats up to a higher boiling point, then releases more steam, further increasing the pressure. This continues until the pressure reaches a set maximum, at which point the pressure cooker starts to release some steam so that the boiling point and pressure remain constant. Thus, the final temperature inside of the can will be 121°C, the boiling point of the water. 19
16. Fried ice cream is a dessert made of a breaded scoop of ice cream that is quickly deep‐fried creating a warm, crispy shell around the still‐cold ice cream. The dessert is commonly made by taking a scoop of ice cream frozen well below the temperature at which ice cream is generally kept, coating it in raw egg, rolling it in cornflakes or cookie crumbs, and briefly deep frying it. A typical recipe suggests heating the oil in a large pot or fryer to 400 degrees F. After this, the coated ice cream balls are lowered one at a time into the oil and fried until golden brown, about 30 seconds. a. [5 pts] Assuming that the heat diffusion constant is the same as water, how far into the ice cream ball does heat diffuse? Explain why it is possible to fry the ice cream in hot oil and serve the dessert still cold inside. L=sqrt (4Dt) D = 1.4 10‐3 cm2/sec t = 30 sec L = sqrt (4*(1.4 10‐3 cm2/sec)*(30 sec)) = 0.41 cm = 4.1 mm Heat only diffuses 4 mm during the 30 sec the ice cream ball is kept in the oil bath, so heat does not diffuse to the center and hence the center stays cold. b. [3 pts] Is it possible to fry an ice cream ball in water instead of oil? Why or why not? If you fried the ice cream in boiling water, the breading on the ice cream would never turn golden‐brown because the temperature would not get higher than 100˚C and not be high enough for browning. You might wind up leaving the ice cream in the bath for more than thirty seconds while trying to brown the breading, which would cause the ice cream inside to melt. 20
17. Marshmallow is an elastic foam that is 80% air trapped in a sweet matrix. In Roald Dahl's Charlie and the Chocolate Factory the idea of marshmallow pillows was suggested. a. [5 pts] Given that an average radius of an air bubble is 0.5mm and the surface tension is 9.5N/m. Calculate the elasticity of the pillow. E=sigma*(phi‐phi_c)/R 9.5*(0.8‐0.64)/0.0005=3 kPa b. [4 pts] The Oompa‐Loompas (the chubby employees of the factory) use the marshmallow pillows as mattresses to sleep on. Each mattress has the dimensions of a cube 1m x 1m x 1m and the workers weigh 50kg each. Calculate how much the pillow compresses when an Oompa‐Loompa sleeps on it (assume g=10m/s2 and that the weight of the Oompa‐Loompa spreads evenly on the mattress). E=F/A / delta‐L/L, F=mg hence: delta‐L=mgL/AE delta‐L = ((50kg* 10m/s2)*1m)/((1m* 1m)*3000 Pa) = 0.17m = 17 cm 21
SCRATCH PAPER 22