Content check — College Physics, Chapter 14: Heat and Heat Transfer Methods

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 14: Heat and Heat Transfer Methods

41 problems · 2 figures

On a hot day, the temperature of an 80,000-L swimming pool increases by

1 . 50ºC

. What is the net heat transfer during this heating? Ignore any complications, such as loss of water by evaporation.

Answer

5 . 02 \times 10^{8} J

14-3 §14.2 source ↗

To sterilize a 50.0-g glass baby bottle, we must raise its temperature from

22.0 ºC

95 . 0º C

. How much heat transfer is required?

Answer

3. 07 \times 10^{3} J

14-5 §14.2 source ↗

Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 20 rubs, at a distance of 7.50 cm per rub, and with an average frictional force of 40.0 N, what is the temperature increase? The mass of tissues warmed is only 0.100 kg, mostly in the palms and fingers.

Answer

0 . 171º C

14-7 §14.2 source ↗

Suppose identical amounts of heat transfer into different masses of copper and water, causing identical changes in temperature. What is the ratio of the mass of copper to water?

Answer

10.8

14-9 §14.2 source ↗

Following vigorous exercise, the body temperature of an 80.0-kg person is

40 . 0º C

. At what rate in watts must the person transfer thermal energy to reduce the the body temperature to

37 . 0º C

in 30.0 min, assuming the body continues to produce energy at the rate of 150 W?

1 watt = 1 joule/second or 1 W = 1 J/s

Answer

617 W

14-11 §14.3 source ↗

How much heat transfer (in kilocalories) is required to thaw a 0.450-kg package of frozen vegetables originally at

0º C

if their heat of fusion is the same as that of water?

Answer

35.9 kcal

14-13 §14.3 source ↗

(a) How much heat transfer is required to raise the temperature of a 0.750-kg aluminum pot containing 2.50 kg of water from

30 . 0º C

to the boiling point and then boil away 0.750 kg of water? (b) How long does this take if the rate of heat transfer is 500 W

1 watt = 1 joule/second (1 W = 1 J/s)

Answer

(a) 591 kcal

(b) $4 . 94 \times 10^{3} s$

14-15 §14.3 source ↗

On a trip, you notice that a 3.50-kg bag of ice lasts an average of one day in your cooler. What is the average power in watts entering the ice if it starts at

0º C

and completely melts to

0º C

water in exactly one day

1 watt = 1 joule/second (1 W = 1 J/s)

Answer

13.5 W

14-17 §14.3 source ↗

(a) How much heat transfer is necessary to raise the temperature of a 0.200-kg piece of ice from

- 20. 0º C

130º C

, including the energy needed for phase changes?
(b) How much time is required for each stage, assuming a constant 20.0 kJ/s rate of heat transfer?
(c) Make a graph of temperature versus time for this process.

Answer

(a) 148 kcal

(b) 0.418 s, 3.34 s, 4.19 s, 22.6 s, 0.456 s

14-19 §14.3 source ↗

How many grams of coffee must evaporate from 350 g of coffee in a 100-g glass cup to cool the coffee from

95 . 0º C

45 . 0º C

? You may assume the coffee has the same thermal properties as water and that the average heat of vaporization is 2340 kJ/kg (560 cal/g). (You may neglect the change in mass of the coffee as it cools, which will give you an answer that is slightly larger than correct.)

Answer

33.0 g

14-20 §14.3 source ↗

(a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases

2 . 80 \times 10^{7} J

of energy when burned. To illustrate this difficulty, calculate the number of liters of water that must be expended to absorb the energy released by burning 1.00 L of crude oil, if the water has its temperature raised from

20 . 0º C

100º C

, it boils, and the resulting steam is raised to

300º C

. (b) Discuss additional complications caused by the fact that crude oil has a smaller density than water.

Answer

(a) 9.67 L

(b) Crude oil is less dense than water, so it floats on top of the water, thereby exposing it to the oxygen in the air, which it uses to burn. Also, if the water is under the oil, it is less efficient in absorbing the heat generated by the oil.

14-22 §14.3 source ↗

To help prevent frost damage, 4.00 kg of $0º C$ water is sprayed onto a fruit tree.

(a) How much heat transfer occurs as the water freezes?

(b) How much would the temperature of the 200-kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be $3 .35 kJ/kg \cdotº C$ , and assume that no phase change occurs.

Answer

a) 319 kcal

b) $2 . 00º C$

14-24 §14.3 source ↗

A 0.0500-kg ice cube at

- 30 . 0º C

is placed in 0.400 kg of

35 . 0º C

water in a very well-insulated container. What is the final temperature?

Answer

20.6º C

14-26 §14.3 source ↗

Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of

500º C

rock must be placed in 4.00 kg of

15 . 0º C

water to bring its temperature to

100º C

, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings and take the average specific heat of the rocks to be that of granite.

Answer

4.38 kg

14-28 §14.3 source ↗

In some countries, liquid nitrogen is used on dairy trucks instead of mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid nitrogen, which has a density of $808 {kg/m}^{3}$ .

(a) Calculate the heat transfer necessary to evaporate this amount of liquid nitrogen and raise its temperature to $3 . 00º C$ . (Use $c_{p}$ and assume it is constant over the temperature range.) This value is the amount of cooling the liquid nitrogen supplies.

(b) What is this heat transfer rate in kilowatt-hours?

(c) Compare the amount of cooling obtained from melting an identical mass of $0º C$ ice with that from evaporating the liquid nitrogen.

Answer

(a) $1 . 57 \times 10^{4} kcal$

(b) $18 .3 kW \cdot h$

14-30 §14.5 source ↗

(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is

120 m^{2}

and their inside surface is at

18. 0º C

, while their outside surface is at

5 .00º C

. (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?

Answer

(a) $1.01 \times 10^{3}$ W

(b) One

14-32 §14.5 source ↗

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is

37 . 0º C

, the skin temperature is

34 . 0º C

, the thickness of the tissues between averages

1 .00 cm

, and the surface area is

1.40 m^{2}

Answer

84.0 W

14-34 §14.5 source ↗

A man consumes 3000 kcal of food in one day, converting most of it to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?

Answer

2.59 kg

14-36 §14.5 source ↗

(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a

1 . {40-m}^{2}

surface area? Assume that the animal’s skin temperature is

32 . 0º C

, that the air temperature is

- 5 . 00º C

, and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?

Answer

(a) 39.7 W

(b) 820 kcal

14-38 §14.5 source ↗

Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of

10.0 m^{2}

and a thermal conductivity twice that of glass wool with the rate of heat conduction through a window that is 0.750 cm thick and that has an area of

2.00 m^{2}

, assuming the same temperature difference across each.

Answer

35 to 1, window to wall

14-40 §14.5 source ↗

Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through the same area and at the same rate as computed in Example 14.6, what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.

Example 14.6 Calculating the Temperature Difference Maintained by a Heat Transfer: Conduction Through an Aluminum Pan in the book ↗

Answer

1 . 05 \times 10^{3} K

14-42 §14.5 source ↗

(a) Calculate the rate of heat conduction through a double-paned window that has a $1.50 {-m}^{2}$ area and is made of two panes of 0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surface temperature is $15 . 0º C$ , while that on the outside is $- 10 . 0º C$ . (Hint: There are identical temperature drops across the two glass panes. First find these and then the temperature drop across the air gap. This problem ignores the increased heat transfer in the air gap due to convection.)

(b) Calculate the rate of heat conduction through a 1.60-cm-thick window of the same area and with the same temperatures. Compare your answer with that for part (a).

Answer

(a) 83 W

(b) 24 times that of a double pane window.

14-44 §14.5 source ↗

For the human body, what is the rate of heat transfer by conduction through the body’s tissue with the following conditions: the tissue thickness is 3.00 cm, the change in temperature is

2 . 00º C

, and the skin area is

1.50 m^{2}

. How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)

Answer

20.0 W, 17.2% of 2400 kcal per day

14-45 §14.6 source ↗

At what wind speed does

- 10º C

air cause the same chill factor as still air at

- 29º C

Answer

10 m/s

14-47 §14.6 source ↗

The “steam” above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 250 g of hot coffee initially at

90 . 0ºC

if 2.00 g evaporates from it? The coffee is in a Styrofoam cup, so other methods of heat transfer can be neglected.

Answer

85.7º C

14-49 §14.6 source ↗

On a hot dry day, evaporation from a lake has just enough heat transfer to balance the

1.00 {kW/m}^{2}

of incoming heat from the Sun. What mass of water evaporates in 1.00 h from each square meter? Explicitly show how you follow the steps in the Problem-Solving Strategies for the Effects of Heat Transfer.

Answer

1.48 kg

14-51 §14.6 source ↗

The Kilauea volcano in Hawaii is the world’s most active, disgorging about

5 \times 10^{5} m^{3}

1200ºC

lava per day. What is the rate of heat transfer out of Earth by convection if this lava has a density of

2700 {kg/m}^{3}

and eventually cools to

30ºC

? Assume that the specific heat of lava is the same as that of granite.

A view of a lava flow on the Kilauea volcano of Hawaii. — Figure 14.34 in the book ↗

Answer

2 \times 10^{4} MW

14-53 §14.6 source ↗

A person inhales and exhales 2.00 L of $37 . 0ºC$ air, evaporating $4 . 00 \times 10^{- 2} g$ of water from the lungs and breathing passages with each breath.

(a) How much heat transfer occurs due to evaporation in each breath?

(b) What is the rate of heat transfer in watts if the person is breathing at a moderate rate of 18.0 breaths per minute?

(d) Discuss the total rate of heat transfer as it relates to typical metabolic rates. Will this breathing be a major form of heat transfer for this person?

Answer

(a) 97.2 J

(b) 29.2 W

(d) The total rate of heat loss would be $29.2 W +$ $9.49 W =$ $38.7 W$ . While sleeping, our body consumes 83 W of power, while sitting it consumes 120 to 210 W. Therefore, the total rate of heat loss from breathing will not be a major form of heat loss for this person.

14-55 §14.7 source ↗

At what net rate does heat radiate from a

275 {-m}^{2}

black roof on a night when the roof’s temperature is

30. 0º C

and the surrounding temperature is

15. 0º C

? The emissivity of the roof is 0.900.

Answer

-

21.7 kW

Note that the negative answer implies heat loss to the surroundings.

14-57 §14.7 source ↗

Radiation makes it impossible to stand close to a hot lava flow. Calculate the rate of heat transfer by radiation from

1.00 m^{2}

1200º C

fresh lava into

30 . 0º C

surroundings, assuming lava’s emissivity is 1.00.

Answer

-

266 kW

14-59 §14.7 source ↗

Find the net rate of heat transfer by radiation from a skier standing in the shade, given the following. She is completely clothed in white (head to foot, including a ski mask), the clothes have an emissivity of 0.200 and a surface temperature of

10 . 0º C

, the surroundings are at

- 15 . 0ºC

, and her surface area is

1.60 m^{2}

Answer

-

36.0 W

14-61 §14.7 source ↗

Thermography is a technique for measuring radiant heat and detecting variations in surface temperatures that may be medically, environmentally, or militarily meaningful.(a) What is the percent increase in the rate of heat transfer by radiation from a given area at a temperature of

34.0ºC

compared with that at

33 . 0ºC

, such as on a person’s skin? (b) What is the percent increase in the rate of heat transfer by radiation from a given area at a temperature of

34.0ºC

compared with that at

20.0ºC

, such as for warm and cool automobile hoods?

A thermograph of the chest area of a patient is shown. There are different colors showing different thermal regions. — Figure 14.35 in the book ↗

Answer

(a) 1.31%

(b) 20.5%

14-63 §14.7 source ↗

A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at

1200ºC

, its surface is at

450ºC

, and the surroundings are at

27 . 0ºC

. (a) Calculate the rate at which energy is transferred by radiation from

1.00 m^{2}

of surface lava into the surroundings, assuming the emissivity is 1.00. (b) Suppose heat conduction to the surface occurs at the same rate. What is the thickness of the lava between the

450ºC

surface and the

1200ºC

interior, assuming that the lava’s conductivity is the same as that of brick?

Answer

(a) $-$ $15.0 kW$

(b) 4.2 cm

14-65 §14.7 source ↗

(a) A shirtless rider under a circus tent feels the heat radiating from the sunlit portion of the tent. Calculate the temperature of the tent canvas based on the following information: The shirtless rider’s skin temperature is

34 . 0ºC

and has an emissivity of 0.970. The exposed area of skin is

0.400 m^{2}

. He receives radiation at the rate of 20.0 W—half what you would calculate if the entire region behind him was hot. The rest of the surroundings are at

34 . 0ºC

. (b) Discuss how this situation would change if the sunlit side of the tent was nearly pure white and if the rider was covered by a white tunic.

Answer

(a) $48 . 5º C$

(b) A pure white object reflects more of the radiant energy that hits it, so a white tent would prevent more of the sunlight from heating up the inside of the tent, and the white tunic would prevent that heat which entered the tent from heating the rider. Therefore, with a white tent, the temperature would be lower than $48 . 5º C$ , and the rate of radiant heat transferred to the rider would be less than 20.0 W.

14-67 §14.7 source ↗

Integrated Concepts

Large meteors sometimes strike the Earth, converting most of their kinetic energy into thermal energy. (a) What is the kinetic energy of a $10^{9} kg$ meteor moving at 25.0 km/s? (b) If this meteor lands in a deep ocean and $80%$ of its kinetic energy goes into heating water, how many kilograms of water could it raise by $5 . 0ºC?$ (c) Discuss how the energy of the meteor is more likely to be deposited in the ocean and the likely effects of that energy.

Answer

(a) $3 \times 10^{17} J$

(b) $1 \times 10^{13} kg$

(c) When a large meteor hits the ocean, it causes great tidal waves, dissipating large amount of its energy in the form of kinetic energy of the water.

14-69 §14.7 source ↗

Integrated Concepts

(a) A large electrical power facility produces 1600 MW of “waste heat,” which is dissipated to the environment in cooling towers by warming air flowing through the towers by $5 . 00ºC$ . What is the necessary flow rate of air in $m^{3} /s$ ? (b) Is your result consistent with the large cooling towers used by many large electrical power plants?

Answer

(a) $3 . 44 \times 10^{5} m^{3} /s$

(b) This is equivalent to 12 million cubic feet of air per second. That is tremendous. This is too large to be dissipated by heating the air by only $5º C$ . Many of these cooling towers use the circulation of cooler air over warmer water to increase the rate of evaporation. This would allow much smaller amounts of air necessary to remove such a large amount of heat because evaporation removes larger quantities of heat than was considered in part (a).

14-71 §14.7 source ↗

Integrated Concepts

A 76.0-kg person suffering from hypothermia comes indoors and shivers vigorously. How long does it take the heat transfer to increase the person’s body temperature by $2 . 00ºC$ if all other forms of heat transfer are balanced?

Answer

20.9 min

14-73 §14.7 source ↗

Integrated Concepts

Heat transfers from your lungs and breathing passages by evaporating water. (a) Calculate the maximum number of grams of water that can be evaporated when you inhale 1.50 L of $37º C$ air with an original relative humidity of 40.0%. (Assume that body temperature is also $37º C$ .) (b) How many joules of energy are required to evaporate this amount? (c) What is the rate of heat transfer in watts from this method, if you breathe at a normal resting rate of 10.0 breaths per minute?

Answer

(a) 3.96×10^-2 g

(b) 96.2 J

14-75 §14.7 source ↗

Integrated Concepts

Hot air rises because it has expanded. It then displaces a greater volume of cold air, which increases the buoyant force on it. (a) Calculate the ratio of the buoyant force to the weight of $50.0º C$ air surrounded by $20.0º C$ air. (b) What energy is needed to cause $1.00 m^{3}$ of air to go from $20.0º C$ to $50.0º C$ ? (c) What gravitational potential energy is gained by this volume of air if it rises 1.00 m? Will this cause a significant cooling of the air?

Answer

(a) 1.102

(b) $2.79 \times 10^{4} J$

(c) 12.6 J. This will not cause a significant cooling of the air because it is much less than the energy found in part (b), which is the energy required to warm the air from $20.0º C$ to $50.0º C$ .

14-76 §14.7 source ↗

Unreasonable Results

(a) What is the temperature increase of an 80.0 kg person who consumes 2500 kcal of food in one day with 95.0% of the energy transferred as heat to the body? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?

Answer

(a) $36º C$

(b) Any temperature increase greater than about $3º C$ would be unreasonably large. In this case the final temperature of the person would rise to $73º C (163º F)$ .

14-78 §14.7 source ↗

Unreasonable Results

(a) Calculate the rate of heat transfer by conduction through a window with an area of $1 .00 m^{2}$ that is 0.750 cm thick, if its inner surface is at $22.0ºC$ and its outer surface is at $35.0ºC$ . (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?

Answer

(a) 1.46 kW

(b) Very high power loss through a window. An electric heater of this power can keep an entire room warm.

(c) The surface temperatures of the window do not differ by as great an amount as assumed. The inner surface will be warmer, and the outer surface will be cooler.

Loading chapter 15…

Problems and answers are adapted from College Physics 2e by Paul Peter Urone, Roger Hinrichs, Kim Dirks and Manjula Sharma, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.