- To take a break from studying physics, you rent the video
of the movie version of the book
*Fahrenheit 451*, which stared Oscar Werner. The setting (in England) is an Orwellian society where books are banned and all information is disseminated by a large TV screen in each home. Fire departments respond not to put out fires, but to burn books, which combust at a temperature of 451 oF (hence the name of the film). In the middle of the film, your mind wanders. You imagine the fire department using the burning books to heat 600 cm3 of water for their afternoon tea. You imagine that the burner transfers 80% of the heat from the burning books to the water, which you remember has a heat capacity of 1.0 calorie/g oC. How much will the water temperature rise from burning one copy of the 500-page book*Fahrenheit 451*if the heat of combustion is 1.0 calorie per page?

- You are helping a friend who is a veterinarian to do some
minor surgery on a cow. She has asked you to sterilize a
scalpel and a hemostat by boiling them for 30 minutes.
You boil them as ordered and then quickly transfer the
instruments to a well insulated tray containing 200 grams
of sterilized water at room temperature (23 oC) which is
just enough to cover the instruments. After a few minutes
the instruments and water will come to the same
temperature, but will they be safe to hand to your friend
without being burned? You are both wearing surgical
rubber gloves, but they are very thin. You know that both
the 50 gram scalpel and the 70 gram hemostat are made
from steel which has a specific heat of 450 J / (kg oC).
They were boiled in 2.0 kg of water with a specific heat
of 4200 J / (kg oC).

- You have a summer job with a company that designs
cookware. Your group is assigned the task of designing a
better pasta pot. You are very excited by a new strong,
light alloy the group has just produced, but will it make
a good pasta pot? If it takes more than 10 minutes to
boil water in a pasta pot, it probably won't sell. So
your boss asks you to calculate how long it would take
water at room temperature (23 oC) to reach boiling
temperature (100 oC) in a pot made of the new alloy. Your
colleagues tell you that a typical pasta pot holds about
2 liters (2.0 kg) of water. They estimate that a pot made
of the alloy would have a mass of 550 grams, and a
specific heat capacity of 860 J / (kg oC). You look in
your physics book and find that water has a specific heat
capacity of 4200 J / (kg oC) and its heat of vaporization
is 2.3 x 106 J/kg. The owner's manual states that the
burners on your stove deliver 1000 Joules of heat per
second. You estimate that only about 20% of this heat is
radiated away.

- You are planning a birthday party for your niece and need
to make at least 4 gallons of Kool-Aid, which you would
like to cool down to 32 oF (0 oC) before the party
begins. Unfortunately, your refrigerator is already so
full of treats that you know there will be no room for
the Kool-Aid. So, with a sudden flash of insight, you
decide to start with 4 gallons of the coldest tap water
you can get, which you determine is 50 oF (10 oC), and
then cool it down with a 1-quart chunk of ice you already
have in your freezer. The owner's manual for your
refrigerator states that when the freezer setting is on
high, the temperature is -20 oC. Will your plan work? You
assume that the density of the Kool-Aid is about the same
as the density of water. You look in your physics book
and find that the density of water is 1.0 g/cm3, the
density of ice is 0.9 g/cm3, the heat capacity of water
is 4200 J / (kg oC), the heat capacity of ice is 2100 J /
(kg oC), the heat of fusion of water is 3.4 x 105 J/kg,
and its heat of vaporization is 2.3 x 106 J/kg.

- You are thinking ahead to spring when one of your friends
is having an outdoor wedding. Your plan is to design the
perfect lemonade for the event. The problem with lemonade
is that you make it at room temperature and then add ice
to cool it to a pleasant 10 ºC. Usually, the ice melts
diluting the lemonade too much. To help you solve this
problem, you look up the specific heat capacity of water
(1.0 cal/(gm ºC)), the specific heat capacity of ice
(0.50 cal/(gm ºC)), and the latent heat of fusion of
water (80 cal/gm). You assume that the specific heat
capacity of the lemonade is the same as water. Since you
will cool your lemonade in a Thermos jug, assume no heat
is added to the lemonade from the environment. Using that
information, you calculate how much water you get from
all the ice melting if you make 6 quarts (5.6 kg) of
lemonade at room temperature (23 ºC) and add ice which
comes straight from the freezer at -5.0 ºC.

- While working for a grain loading company over the
summer, your boss asks you to determine the efficiency of
a new type of pneumatic elevator. The elevator is
supported in a cylindrical shaft by a column of air,
which you assume to be an ideal gas with a specific heat
of 12.5 J/mol-ºC. The air pressure in the column is 1.2
x 105 Pa when the elevator carries no load. The bottom of
the cylindrical shaft opens out so that there is a
reservoir of air at room temperature (25º C) below the
elevator when it begins loading. Seals around the
elevator assure that no air escapes as the elevator moves
up and down. The elevator has a cross-sectional area of
10 m2. A cycle of elevator use begins with the unloaded
elevator. The elevator is then loaded with 20,000 kg of
grain while the air temperature stays at 25º C causing
the elevator to sink. The air in the system is then
heated to 75º C and the elevator rises. The elevator is
then unloaded, while the air remains at 75º C. Finally,
the air in the system is cooled to room temperature
again, returning the elevator to its starting level.
While the elevator is moving up and down, you assume that
it moves at a constant velocity so that the pressure in
the gas is constant.

- Note: This problem requires both mechanical energy and
heat energy for a solution. In the class demonstration, a
2.0-gram lead bullet was shot into a 2.0-kg block of
wood. The block of wood with the bullet stuck in it was
hung from a string and rose to a height 0.50 cm above its
initial position. From that information we calculated
that the initial speed of the bullet was about 300 m/s
(close to the speed of sound). What was the bullet like
when it stopped? Using conservation of energy and
conservation of momentum, we decided that the internal
energy of the bullet, block system had increased
substantially. If the change of internal energy of the
bullet was half that of the system, would this change be
enough to melt the bullet? Assume that the bullet had a
temperature of 50 oC when it left the gun. The melting
temperature of lead is 330 oC. It has a specific heat
capacity of 130 J/(kg oC) and a latent heat of fusion of
25 J/g. The specific heat capacity of wood is 1700 J/(kg
oC).