28) A machine part consists of 0.10 kg of iron (of specific heat 470 J/kg ∙ K ) and 0.16 kg of
copper (of specific heat 390 J/kg ∙ K). How much heat must be added to the gear to raise its
temperature from 18°C to 53°C?
A) 910 J
B) 3800 J
C) 4000 J
D) 4400 J
29) An aluminum electric tea kettle with a mass of 500 g is heated with a 500-W heating coil.
How long will it take to heat up 1.0 kg of water from 18°C to 98°C in the tea kettle? The specific
heat of aluminum is 900 J/kg ∙ K and that of water is 4186 J/kg ∙ K.
A) 5.0 minutes
B) 7.0 minutes
C) 12 minutes
D) 15 minutes
E) 18 minutes
30) A carpenter is driving a 15.0-g steel nail into a board. His 1.00-kg hammer is moving at 8.50
m/s when it strikes the nail. Half of the kinetic energy of the hammer is transformed into heat in
the nail and does not flow out of the nail. What is the increase in temperature of the nail after the
three blows that the carpenter needs to drive the nail in completely? The specific heat of steel is
448 J/kg ∙ K.
A) 8.1 K
B) 3.6 K
C) 1.8 K
D) 2.7 K
E) 7.7 K
31) A 5.00-g lead BB moving at 44.0 m/s penetrates a wood block and comes to rest inside the
block. If half of its kinetic energy is absorbed by the BB, what is the change in the temperature
of the BB? The specific heat of lead is 128 J/kg ∙ K.
A) 0.940 K
B) 1.10 K
C) 1.26 K
D) 2.78 K
E) 3.78 K
32) It is necessary to determine the specific heat of an unknown object. The mass of the object is
It is determined experimentally that it takes to raise the temperature What is
the specific heat of the object?
A) 7.46 J/kg ∙ K
B) 1500 J/kg ∙ K
C) 0.00130 J/kg ∙ K
D) 3,020,000 J/kg ∙ K
33) A 920-g empty iron kettle is put on a stove. How much heat in joules must it absorb to raise
its temperature form to The specific heat for iron is 113 cal/kg ∙ C°, and 1 cal =
4.186 J.
A) 33,900 J
B) 40,500 J
C) 8110 J
D) 40,100 J
34) A container of 114.0 g of water is heated using of power, with perfect efficiency. How
long will it take to raise the temperature of the water from to The specific heat
capacity of the container is negligible, and the specific heat capacity of water is 4.186 × 103 J/kg
∙ C.
A) 71 s
B) 4.1 s
C) 17 s
D) 320,000 s
35) A 6.5-g iron meteor hits the earth at a speed of 295 m/s. If its kinetic energy is entirely
converted to heat in the meteor, by how much will its temperature rise? The specific heat of iron
is 113 cal/kg ∙ C°, and 1 cal = 4.186 J.
A) 92.0 C°
B) 57,100 C°
C) 0.147 C°
D) 384 C°
36) A glass beaker of unknown mass contains of water. The system absorbs of
heat and the temperature rises as a result. What is the mass of the beaker? The specific
heat of glass is 0.18 cal/g ∙ °C, and that of water is 1.0 cal/g ∙ C°.
A) 140 g
B) 560 g
C) 540 g
D) 270,000 g
37) On his honeymoon, James Joule attempted to explore the relationships between various
forms of energy by measuring the rise of temperature of water which had fallen down a waterfall
on Mount Blanc. What maximum temperature rise would one expect for a waterfall with a
vertical drop of 20 m? The specific heat of water is 4186 J/kg ∙ K.
A) 0.047 C°
B) 0.053 C°
C) 0.064 C°
D) 0.071 C°
38) The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational
potential energy is converted to thermal energy, by what temperature does the water rise? The
specific heat of water is 4186 J/kg ∙ K.
A) 0.10 C°
B) 0.12 C°
C) 0.37 C°
D) 0.42 C°
39) In a flask, 114.0 g of water is heated using of power, with perfect efficiency. How
long will it take to raise the temperature of the water from to The specific heat of
water is 4186 J/kg ∙ K.
A) 71 s
B) 4.1 s
C) 17 s
D) 320,000 s
40) A 200-L electric water heater uses 2.0 kW. Assuming no heat loss, how many hours would
it take to heat the water in this tank from 23°C to 75°C? The specific heat of water is 4186 J/kg ∙
K and its density is 1000 kg/m3.
A) 5.0. hours
B) 6.0 hours
C) 7.0 hours
D) 8.0 hours
41) In grinding a steel knife, the metal can get as hot as 400°C. If the blade has a mass of 80 g,
what is the minimum amount of water needed at 20°C if the water is to remain liquid and not rise
above 100°C when the hot blade is quenched in it? The specific heat of the steel is 0.11 cal/g ∙ C°
and the specific heat of water is 1.0 cal/g ∙ C°.
A) 22 g
B) 33 g
C) 44 g
D) 55 g
42) How much heat must be removed from 456 g of water at 25.0°C to change it into ice at –
10.0°C? The specific heat of ice is 2090 J/kg ∙ K, the latent heat of fusion of water is 33.5 × 104
J/kg, and the specific heat of water is 4186 J/kg ∙ K.
A) 105 kJ
B) 153 kJ
C) 57.3 kJ
D) 47.7 kJ
E) 210 kJ
43) A runner generates 1260 W of thermal energy. If this heat has to be removed only by
evaporation, how much water does this runner lose in 15 minutes of running? The latent heat of
vaporization of water is 22.6 × 105 J/kg.
A) 50 g
B) 500 g
C) 35 g
D) 350 g
E) 40 g
44) If you add 700 kJ of heat to 700 g of water originally at 70.0°C, how much water is left in
the container? The latent heat of vaporization of water is 22.6 × J/kg, and its specific heat
capacity is 4186 J/kg ∙ K.
A) 429 g
B) 258 g
C) 340 g
D) 600 g
E) none
45) If you add 1.33 MJ of heat to 500 g of water at 50°C in a sealed container, what is the final
temperature of the steam? The latent heat of vaporization of water is 22.6 × 105 J/kg, the
specific heat of steam is 2010 J/kg ∙ K, and the specific heat of water is 4186 J/kg ∙ K.
A) 100°C
B) 112°C
C) 123°C
D) 147°C
E) 195°C
46) A 2294-kg sample of water at 0° C is cooled to and freezes in the process. How much
heat is liberated? For water LF = 334,000 J/kg and LV = 2.256 × 106 J/kg. The specific heat of
ice is 2050 J/kg ∙ K.
A) 935,000 kJ
B) 597,000 kJ
C) 1,110,000 kJ
D) 334,000 kJ
47) The melting point of aluminum is 660°C, its latent heat of fusion is 4.00 × 105 J/kg, and its
specific heat is 900J/kg ∙ K. How much heat must be added to 500 g of aluminum originally at
27°C to completely melt it?
A) 485 kJ
B) 395 kJ
C) 273 kJ
D) 147 kJ
E) 14 kJ
48) A metal has a latent heat of fusion of 2.32 × 104 J/kg, a specific heat of 128 J/kg ∙ K, and a
melting point of 228°C. A 30-g pellet of this metal at 16°C hits a solid wall and comes to a
complete stop. What would the speed of the pellet have to be in order for it to melt completely
when it hits the wall, assuming that all of its kinetic energy is transformed into heat within the
pellet?
A) 207 m/s
B) 215 m/s
C) 232 m/s
D) 273 m/s
E) 317 m/s
49) Solar houses use a variety of energy storage devices to retain the heat absorbed during the
day so that it can be released during the night. Suppose that you were to use a device of this kind
to produce steam at 100°C during the day, and then allow the steam to cool to 0°C and freeze
during the night. How many kilograms of water would be needed to store 20.0 kWh of energy in
this way? The latent heat of vaporization of water is 22.6 × 105 J/kg, the latent heat of fusion of
water is 33.5 × 104 J/kg, and the specific heat capacity of water is 4186 J/kg ∙ K.
A) 12.4 kg
B) 23.9 kg
C) 35.7 kg
D) 42.6 kg
E) 54.2 kg
50) A beaker of negligible heat capacity contains 456 g of ice at -25.0°C. A lab technician begins
to supply heat to the container at the rate of 1000 J/min. How long after starting will the ice
begin to melt, assuming all of the ice has the same temperature? The specific heat of ice is 2090
J/kg ∙ K and the latent heat of fusion of water is 33.5 × 104 J/kg.
51) A beaker of negligible heat capacity contains 456 g of ice at -25.0°C. A lab technician begins
to supply heat to the container at the rate of 1000 J/min. How long after starting will it take
before the temperature starts to rise above 0°C? The specific heat of ice is 2090 J/kg ∙ K and the
latent heat of fusion of water is 33.5 × 104 J/kg.
52) The melting point of aluminum is 660°C, its latent heat of fusion is 4.00 × 105 J/kg, and its
specific heat is 900 J/kg ∙ K. If 300 kJ of heat are added to 442 g of aluminum at 100°C, what is
the final state of the system? That is, how much is liquid, how much is solid, and what is its
temperature?
53) A 45.0-kg sample of ice is at 0.00° C. How much heat is needed to melt it? For water LF =
334,000 J/kg and LV = 2.256 × 106 J/kg.
A) 1.50 × 104 kJ
B) 4.10 × 106 kJ
C) 0.00 kJ
D) 1.02 × 105 kJ
54) Heat is added to a 3.0 kg piece of ice at a rate of How long will it take for the ice at
0.0° C to melt? For water LF = 334,000 J/kg and LV = 2.246 × 106 J/kg.
A) 1.6 s
B) 640,000 s
C) 0.0 s
D) 1000 s
55) A .20-kg ice cube at 0.0°C has sufficient heat added to it to cause total melting, and the
resulting water is heated to How much heat is added? For water LF = 334,000 J/kg, LV =
2.256 × 106 J/kg, the c = 4.186 x 103 J/kg ∙ C.
A) 130 kJ
B) 14,000 kJ
C) 81 kJ
D) 59 kJ
56) How much heat must be added to a 8.0-kg block of ice at -8°C to change it to water at
The specific heat of ice is 2050 J/kg ∙ C°, the specific heat of water is 4186 J/kg ∙ C°, the latent
heat of fusion of ice is 334,000 J/kg, and 1 cal = 4.186 J.
A) 780 kcal
B) 140 kcal
C) 180 kcal
D) 810 kcal
E) 730 kcal
57) When a sample of water at 0.0°C is cooled to –36.0°C and freezes in the process, 935,000 kJ
of heat is liberated. What is the mass of this sample of water? For water LF = 334,000 J/kg, LV =
2.256 × 106 J/kg, and the specific heat of ice is 2050 J/kg ∙ C°.
A) 2290 kg
B) 1145 kg
C) 2800 kg
D) 12,700 kg
58) A 771.0-kg copper bar is put into a smelter for melting. The initial temperature of the copper
is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? The
specific heat for copper is 386 J/kg∙K, the heat of fusion for copper is 205,000 J/kg, and its
melting point is 1357 K.
A) 4.73 × 105 kJ
B) 3.15 × 1011 kJ
C) 3.15 × 108 kJ
D) 5.62 × 105 kJ
59) A substance has a melting point of 20°C and a heat of fusion of 3.4 × J/kg. The boiling
point is and the heat of vaporization is at a pressure of one atmosphere. The
specific heats for the solid, liquid, and gaseous phases are 600 J/kg ∙ K (solid), 1000 J/kg ∙ K
(liquid), and 400 J/kg ∙ K (gaseous). How much heat is required to raise the temperature of
of this substance from to at a pressure of one atmosphere?
A) 260 kJ
B) 190 kJ
C) 230 kJ
D) 92 kJ
E) 320 kJ
60) A substance has a melting point of 20°C and a heat of fusion of The boiling
point is and the heat of vaporization is at a pressure of one atmosphere. The
specific heats for the solid, liquid, and gaseous phases are 600 J/kg ∙ K (solid), 1000 J/kg ∙ K
(liquid), and 400 J/kg ∙ K (gaseous). How much heat is given up by of this substance
when it is cooled from 170°C to 86°C at a pressure of one atmosphere?
A) 400 kJ
B) 200 kJ
C) 300 kJ
D) 440 kJ
E) 640 kJ
61) A person tries to heat up her bath water by adding 5.0 L of water at 80°C to 60 L of water at
30°C. What is the final temperature of the bath water?
A) 34°C
B) 36°C
C) 38°C
D) 40°C
62) If 50 g of lead (of specific heat 0.11 kcal/kg ∙ C°) at 100°C is put into 75 g of water (of
specific heat 1.0 kcal/kg ∙ C°) at 0°C. What is the final temperature of the mixture?
A) 2.0°C
B) 6.8°C
C) 25°C
D) 50°C
63) A lab assistant pours 330 g of water at 45°C into an 855-g aluminum container that is at an
initial temperature of 10°C. The specific heat of aluminum is and that of water is 4186
J/kg ∙ K. What is the final temperature of the system, assuming no heat is exchanged with the
surroundings?
A) 28°C
B) 32°C
C) 31°C
D) 33°C
E) 35°C
64) A 90-g aluminum calorimeter contains 390 g of water at an equilibrium temperature of
A piece of metal, initially at is added to the calorimeter. The final temperature at
equilibrium is 32° C. Assume there is no external heat exchange. The specific heat capacities of
aluminum and water are 910 J/kg ∙ K (aluminum) and 4190 J/kg ∙ K (water). What is the specific
heat capacity of the 160-g piece of metal?
A) 470 J/kg ∙ K
B) 430 J/kg ∙ K
C) 350 J/kg ∙ K
D) 310 J/kg ∙ K
E) 510 J/kg ∙ K
65) A camper is about to drink his morning coffee. He pours 400 grams of coffee, initially at
75°C into a 250-g aluminum cup, initially at 16°C. What is the equilibrium temperature of the
coffee-cup system, assuming no heat is lost to the surroundings? The specific heat of aluminum
is 900 J/kg ∙ K, and the specific heat of coffee is essentially the same as that of water, which is
4186 J/kg ∙ K.
A) 45°C
B) 62°C
C) 65°C
D) 68°C
E) 71°C
66) A lab student drops a 400.0-g piece of metal at 120.0°C into a cup containing 450.0 g of
water at 15.0°C. After waiting for a few minutes, the student measures that the final temperature
of the system is 40.0°C. What is the specific heat of the metal, assuming that no significant heat
is exchanged with the surroundings or the cup? The specific heat of water is 4186 J/kg ∙ K.
A) 1470 J/kg ∙ K
B) 2830 J/kg ∙ K
C) 3420 J/kg ∙ K
D) 3780 J/kg ∙ K
E) 4280 J/kg ∙ K
67) A lab assistant drops a 400.0-g piece of metal at 100.0°C into a 100.0-g aluminum cup
containing 500.0 g of water at In a few minutes, she measures the final temperature of the
system to be 40.0°C. What is the specific heat of the 400.0-g piece of metal, assuming that no
significant heat is exchanged with the surroundings? The specific heat of this aluminum is 900.0
J/kg ∙ K and that of water is 4186 J/kg ∙ K.
A) 1900 J/kg ∙ K
B) 2270 J/kg ∙ K
C) 3300 J/kg ∙ K
D) 3800 J/kg ∙ K
E) 4280 J/kg ∙ K
68) A jogger is running outdoors on a cold day when the temperature is -20.0°C. She is breathing
at the rate of 25 breaths per minute, and each time she breathes in she inhales 0.00450 m3 of air.
How much heat does she lose from breathing during 20.0 minutes of jogging if the air in her
lungs is heated to her body temperature of 37.0°C before it is exhaled? The specific heat of air is
1020 J/kg ∙ K and the density of air under typical conditions is 1.29 kg/m3.
A) 169 kJ
B) 278 kJ
C) 354 kJ
D) 431 kJ
E) 543 kJ
69) A person is walking outdoors on a cold day when the temperature is -20°C. He is breathing
at the rate of 16 breaths per minute, and each time he breathes in he inhales 0.0050 m3 of air. At
what rate does he lose heat from breathing if the air in his lungs is heated to body temperature
(37°C) before it is exhaled? The specific heat of air is 1020 J/kg ∙ K and the density of air is 1.29
kg/m3.
A) 60 W
B) 90 W
C) 100 W
D) 150 W
E) 300 W
70) A piece of iron of mass 0.12 kg is taken from an oven where its temperature is 336°C and
quickly placed in an insulated copper can that contains 0.20 kg of water. The copper can has
mass 0.50 kg, and it and the water in it are originally at a temperature of 20°C. Calculate the final
temperature of the system, assuming no heat is lost to the surroundings. Use the following
specific heats: 4190J/kg ∙ C° (water), 470 J/kg ∙ C° (iron), and 390 J/kg ∙ C° (copper).
71) A 0.600-kg piece of metal X is heated to 100°C and placed in an aluminum can of mass
0.200-kg which contains 0.500 kg of water initially at 17.3°C. The final equilibrium temperature
of the mixture is 20.2°C, what is the specific heat of metal X? The specific heats of water and
aluminum are 4186 J/kg ∙ K (water) and 910 J/kg ∙ K (aluminum).
A) 140 J/kg ∙ K
B) 270 J/kg ∙ K
C) 450 J/kg ∙ K
D) 900 J/kg ∙ K
72) When 50 g of a certain material at 100°C is mixed with 100 g of water at 0°C, the final
temperature is 40°C. What is the specific heat of the material? The specific heat of water is 1.00
kcal/kg ∙ C°.
A) 0.33 kcal/kg ∙ C°
B) 0.75 kcal/kg ∙ C°
C) 1.3 kcal/kg ∙ C°
D) 7.5 kcal/kg ∙ C°
73) A person makes iced tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many
kilograms of ice, initially at 0°C, are required to bring the mixture to 10°C? The specific heat of
water (and tea) is 4186 J/kg ∙ K, and the latent heat of fusion of ice is 3.34 × 105 J/kg.
A) 1.0 kg
B) 1.2 kg
C) 1.4 kg
D) 1.7 kg
74) A 600-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity
containing 100 g of ice at 0°C and 120 g of water, also at 0°C. What is the final temperature of
the system? The specific heat of iron is 448 J/kg ∙ K, the latent heat of fusion of water is 33.5 ×
104 J/kg, and the specific heat of water is 4186 J/kg ∙ K.
75) A 35-g block of ice at -14°C is dropped into a calorimeter (of negligible heat capacity)
containing 400 g of water at 0°C. When the system reaches equilibrium, how much ice is left in
the calorimeter? The specific heat of ice is 2090 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the
latent heat of fusion of water is 33.5 × 104 J/kg.
A) 32 g
B) 33 g
C) 35 g
D) 38 g
E) 41 g
76) A 44.0-g block of ice at -15.0°C is dropped into a calorimeter (of negligible heat capacity)
containing of water at 5.0°C. When equilibrium is reached, how much of the ice will have
melted? The specific heat of ice is 2090 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent
heat of fusion of water is 33.5 × 104 J/kg.
A) 2.1 g
B) 21 g
C) 5.2 g
D) 52 g
E) 4.4 g
77) A 40.0-g block of ice at -15.00°C is dropped into a calorimeter (of negligible heat capacity)
containing water at 15.00°C. When equilibrium is reached, the final temperature is 8.00°C. How
much water did the calorimeter contain initially? The specific heat of ice is 2090 J/kg ∙ K, that of
water is 4186 J/kg ∙ K, and the latent heat of fusion of water is 33.5 × 104 J/kg.
A) 302 g
B) 345 g
C) 405 g
D) 546 g
E) 634 g
78) A 400-g block of iron at 400°C is dropped into a calorimeter (of negligible heat capacity)
containing 60 g of water at 30°C. How much steam is produced? The latent heat of vaporization
of water is 22.6 × 105 J/kg and its specific heat capacity is 4186 J/kg ∙ K. The average specific
heat of iron over this temperature range is 560 J/kg ∙ K.
A) 22 g
B) 33 g
C) 42 g
D) 54 g
E) 59 g
79) An 920-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity
containing 50 g of ice at 0°C and 92 g of water, also at 0°C. What is the final temperature of the
system? The specific heat of iron is 448 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent
heat of fusion of water is 33.5 × 104 J/kg.
A) 0°C
B) 11°C
C) 14°C
D) 24°C
E) 32°C
80) A 360-g metal container, insulated on the outside, holds 180.0 g of water in thermal
equilibrium at 22.0°C. A 24.0-g ice cube, at the melting point, is dropped into the water, and
when thermal equilibrium is reached the temperature is 15.0°C. Assume there is no heat
exchange with the surroundings. For water, the specific heat capacity is 4190 J/kg ∙ K and the
heat of fusion is 3.34 × 105 J/kg. What is the specific heat capacity of the metal of the container?
A) 1700 J/kg ∙ K
B) 970 J/kg ∙ K
C) 2300 J/kg ∙ K
D) 2800 J/kg ∙ K
E) 3300 J/kg ∙ K
81) Two experimental runs are performed to determine the calorimetric properties of an alcohol
which has a melting point of -10.0° C. In the first run, a 200-g cube of frozen alcohol, at the
melting point, is added to 300 g of water at 20.0°C in a styrofoam container. When thermal
equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run,
an identical cube of alcohol is added to 500 g of water at 20.0°C and the temperature at thermal
equilibrium is 10.0°C. The specific heat capacity of water is 4190 J/kg ∙ K. Assume no heat is
exchanged with the styrofoam container and the surroundings. What is the heat of fusion of the
alcohol?
A) 5.5 × 104 J/kg
B) 6.3 × 104 J/kg
C) 7.1 × 104 J/kg
D) 7.9 × 104 J/kg
E) 8.7 × 104 J/kg
82) Two experimental runs are performed to determine the calorimetric properties of an alcohol
which has a melting point of -10° C. In the first run, a 200-g cube of frozen alcohol, at the
melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal
equilibrium is reached, the alcohol-water solution is at a temperature of 5°C. In the second run,
an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal
equilibrium is 10°C. The specific heat capacity of water is 4190 J/kg ∙ K. Assume no heat is
exchanged with the styrofoam container and the surroundings. What is the specific heat capacity
of the alcohol?
A) 1700 J/kg ∙ K
B) 1900 J/kg ∙ K
C) 2100 J/kg ∙ K
D) 2300 J/kg ∙ K
E) 2500 J/kg ∙ K
83) How many grams of ice at -17°C must be added to 741 grams of water that is initially at a
temperature of to produce water at a final temperature of Assume that no heat is lost to
the surroundings and that the container has negligible mass. The specific heat of liquid water is
4190 J/kg ∙ C° and of ice is 2000 J/kg ∙ C°. For water the normal melting point is 0°C and the
heat of fusion is 334 × 103 J/kg. The normal boiling point is 100°C and the heat of vaporization
is 2.256 × 106 J/kg.
84) A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum
section that is 0.20 m long and a copper section that is long. Both sections have a cross-
sectional area of The aluminum end and the copper end are maintained at
temperatures of and respectively. The thermal conductivities of aluminum and
copper are 205 W/m ∙ K (aluminum) and 385 W/m ∙ K (copper). What is the temperature of the
aluminum-copper junction in the rod with steady state heat flow?
A) 100°C
B) 93°C
C) 86°C
D) 80°C
E) 74°C
85) A heat conducting rod, 1.60 m long and wrapped in insulation, is made of an aluminum
section that is 0.90 m long and a copper section that is long. Both sections have a cross-
sectional area of The aluminum end and the copper end are maintained at
temperatures of and respectively. The thermal conductivities of aluminum and
copper are 205 W/m ∙ K (aluminum) and 385 W/m ∙ K (copper). At what rate is heat conducted
in the rod under steady state conditions?
A) 9.0 W
B) 7.9 W
C) 10 W
D) 11 W
E) 12 W
86) A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of
alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas
of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that for
alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C, and the other end
of the rod is maintained at an unknown temperature. When steady state flow has been
established, the temperature at the junction of the alloys is measured to be 40° C, and the rate of
heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy
B?
A) 80°C
B) 84°C
C) 88°C
D) 92°C
E) 96°C
87) A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of
alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas
of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that for
alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C, and the other end
of the rod is maintained at an unknown temperature. When steady state flow has been
established, the temperature at the junction of the alloys is measured to be 40° C, and the rate of
heat flow in the rod is measured at 56 W. What is the thermal conductivity of alloy A?
A) 120 W/m ∙ K
B) 125 W/m ∙ K
C) 130 W/m ∙ K
D) 135 W/m ∙ K
E) 140 W/m ∙ K
88) Some properties of a certain glass are listed here:
Density 2300 kg/m3
Specific heat capacity 840 J/kg ∙ C°
Coefficient of thermal expansion 8.5 × 10-6 (C°)-1
Thermal conductivity 0.80 W/m ∙ C°
A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner
surface of the glass is and at the outer surface 4°C. How much heat is lost each hour through
the window?
A) 3.1 × 107 J
B) 3.1 × 104 J
C) 8.6 × 103 J
D) 8.6 J
E) 3.1 × 105 J
89) A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick.
The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow
through the wall by 90 percent. The inner surface of the wooden wall is maintained at -10°C and
the outer surface of the concrete wall is at 20°C. The thermal conductivities of concrete and
wood are 0.80 W/m ∙ K (concrete) and 0.040 W/m ∙ K (wood). What is the temperature
difference across the layer of wood?
A) 24 C°
B) 25 C°
C) 26 C°
D) 27 C°
E) 28 C°
90) A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick.
The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow
through the wall by 90 percent. The inner surface of the wooden wall is maintained at -10°C and
the outer surface of the concrete wall is at 20°C. The thermal conductivities of concrete and
wood are 0.80 W/m ∙ K (concrete) and 0.040 W/m ∙ K (wood). What should be the thickness of
the layer of wood?
A) 60 mm
B) 70 mm
C) 80 mm
D) 90 mm
E) 100 mm
91) A solid concrete wall has dimensions 4.0 m × 2.4 m and is 30 cm thick. The thermal
conductivity of the concrete is 1.3 W/m ∙ K, and it separates a basement from the ground
outside. The inner surface of the wall is at 18°C, and the outside surface is at 6°C. How much
heat flows through the wall every hour?
A) 1.8 MJ
B) 1.8 kJ
C) 500 J
D) 5.0 MJ
E) 5.0 kJ
92) A glass tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that
is in contact with the heating element has an area of 0.090 m2 and is 1.5 mm thick. At a certain
moment, the temperature of the water is 75°C, and it is rising at the rate of 3 C° per minute.
What is the temperature of the outside surface of the bottom of the tea kettle? Neglect the heat
capacity of the kettle, and assume that the inner surface of the kettle is at the same temperature as
the water inside. The thermal conductivity of glass is 0.840 W/m ∙ K and the specific heat of
water is 4186 J/kg ∙ K.
A) 39°C
B) 92°C
C) 120°C
D) 86°C
E) 77°C
93) A 400-g stainless steel tea kettle containing 500 g of water is on the stove. The portion of the
tea kettle that is in contact with the heating element has an area of 0.090 m2 and is 2.0 mm thick.
At a certain moment, the temperature of the water is 75°C, and it is rising at the rate of 3.0 C°
per minute. What is the difference in temperature between the inside and the outside of the
bottom of the tea kettle? Assume that the inner surface of the kettle is at the same temperature as
the water inside. The thermal conductivity of stainless steel is 16.3 W/m ∙ K, the specific heat of
the steel is 448 J/kg ∙ K, and the specific heat of water is 4186 J/kg . K.
A) 2.2 C°
B) 1.5 C°
C) 1.1 C°
D) 0.50 C°
E) 0.15 C°
94) Two metal rods, one silver and the other copper, are both immersed at one end in a steam
chamber at a temperature of 100°C. The other end of each one is in an ice water bath at 0°C. The
rods are 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is
exchanged between the rods and the surroundings, except at the ends. How much total heat flows
through the two rods each minute? The thermal conductivity of silver is 417 W/m ∙ K, and that of
copper is 395 W/m ∙ K.
A) 20 kJ
B) 39 kJ
C) 47 kJ
D) 49 kJ
E) 11 kJ
95) Two metal rods, one silver and the other gold, are attached to each other end–to-end. The free
end of the silver rod is immersed in a steam chamber at 100°C, and the free end of the gold rod
in an ice water bath at 0°C. The rods are both 5.0 cm long and have a square cross-section that is
2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the
ends. How much total heat flows through the two rods each minute? The thermal conductivity of
silver is 417 W/m ∙ K, and that of gold is 291 W/m ∙ K.
A) 8.2 kJ
B) 9.5 kJ
C) 12 kJ
D) 14 kJ
E) 16 kJ
96) Two metal rods, one silver and the other gold, are attached to each other end–to-end. The free
end of the silver rod is immersed in a steam chamber at 100°C, and the free end of the gold rod
in an ice water bath at 0°C. The rods are both 5.0 cm long and have a square cross-section that is
2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the
ends. What is the temperature at the point where the two rods are in contact with one another?
The thermal conductivity of silver is 417 W/m ∙ K, and that of gold is 291 W/m ∙ K.
A) 39°C
B) 41°C
C) 47°C
D) 53°C
E) 59°C
97) The thermal conductivity of a certain concrete is 0.80 W/m . K and the thermal conductivity
of a certain wood is 0.10 W/m ∙ K. How thick would a solid concrete wall have to be in order to
have the same rate of heat flow through it as an 8.0-cm thick wall made of solid wood? Both
walls have the same surface area and the same temperature difference across their faces.
A) 53 cm
B) 64 cm
C) 71 cm
D) 85 cm
98) The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and
the other brass) of the same length and cross-sectional area are joined together end to end. The
free end of the brass rod is maintained at 0°C and the free end of the aluminum rod is maintained
at 200°C. If no heat escapes from the sides of the rods, what is the temperature at the place
where the two rods are joined together?
A) 76°C
B) 133°C
C) 148°C
D) 155°C
99) A window glass that is 0.5 cm thick has dimensions of 3 m by 1.5 m. The thermal
conductivity of this glass is 0.8 W/m ∙ K. If the outside surface of the glass is at -10°C and the
inside surface is at 20°C, how much heat flows through the window in every hour?
A) 50 MJ
B) 60 MJ
C) 70 MJ
D) 80 MJ