enough to chill the air next to it. To see just how rapidly the windows
and the resulting steam is raised to 300ºC . (b) Discuss additional
transfer heat by conduction, calculate the rate of conduction in watts
complications caused by the fact that crude oil has a smaller density than
water.
through a 3.00-m2 window that is 0.635 cm thick (1/4 in) if the
21. The energy released from condensation in thunderstorms can be very temperatures of the inner and outer surfaces are 5.00ºC and −10.0ºC
large. Calculate the energy released into the atmosphere for a small
, respectively. This rapid rate will not be maintained—the inner surface
storm of radius 1 km, assuming that 1.0 cm of rain is precipitated
will cool, and even result in frost formation.
uniformly over this area.
32. Calculate the rate of heat conduction out of the human body,
22. To help prevent frost damage, 4.00 kg of 0ºC water is sprayed onto
assuming that the core internal temperature is 37.0ºC , the skin
a fruit tree.
temperature is 34.0ºC , the thickness of the tissues between averages
(a) How much heat transfer occurs as the water freezes?
1.00 cm , and the surface area is 1.40 m2 .
(b) How much would the temperature of the 200-kg tree decrease if this
33. Suppose you stand with one foot on ceramic flooring and one foot on
amount of heat transferred from the tree? Take the specific heat to be
3.35 kJ/kg⋅ºC , and assume that no phase change occurs.
a wool carpet, making contact over an area of 80.0 cm2 with each foot.
Both the ceramic and the carpet are 2.00 cm thick and are 10.0ºC on
23. A 0.250-kg aluminum bowl holding 0.800 kg of soup at 25.0ºC is
their bottom sides. At what rate must heat transfer occur from each foot
placed in a freezer. What is the final temperature if 377 kJ of energy is
to keep the top of the ceramic and carpet at 33.0ºC ?
transferred from the bowl and soup, assuming the soup’s thermal
properties are the same as that of water? Explicitly show how you follow
34. A man consumes 3000 kcal of food in one day, converting most of it
the steps in Problem-Solving Strategies for the Effects of Heat
to maintain body temperature. If he loses half this energy by evaporating
water (through breathing and sweating), how many kilograms of water
evaporate?
24. A 0.0500-kg ice cube at −30.0ºC is placed in 0.400 kg of 35.0ºC
35. (a) A firewalker runs across a bed of hot coals without sustaining
water in a very well-insulated container. What is the final temperature?
burns. Calculate the heat transferred by conduction into the sole of one
25. If you pour 0.0100 kg of 20.0ºC water onto a 1.20-kg block of ice
foot of a firewalker given that the bottom of the foot is a 3.00-mm-thick
callus with a conductivity at the low end of the range for wood and its
(which is initially at −15.0ºC ), what is the final temperature? You may
assume that the water cools so rapidly that effects of the surroundings
density is 300 kg/m3 . The area of contact is 25.0 cm2 , the
are negligible.
temperature of the coals is 700ºC , and the time in contact is 1.00 s.
26. Indigenous people sometimes cook in watertight baskets by placing
hot rocks into water to bring it to a boil. What mass of 500ºC rock must
(b) What temperature increase is produced in the 25.0 cm3 of tissue
be placed in 4.00 kg of 15.0ºC water to bring its temperature to 100ºC
affected?
, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may
(c) What effect do you think this will have on the tissue, keeping in mind
neglect the effects of the surroundings and take the average specific heat
that a callus is made of dead cells?
of the rocks to be that of granite.
36. (a) What is the rate of heat conduction through the 3.00-cm-thick fur
27. What would be the final temperature of the pan and water in
of a large animal having a 1.40-m2 surface area? Assume that the
Calculating the Final Temperature When Heat Is Transferred
animal’s skin temperature is 32.0ºC , that the air temperature is
Between Two Bodies: Pouring Cold Water in a Hot Pan if 0.260 kg of
water was placed in the pan and 0.0100 kg of the water evaporated
−5.00ºC , and that fur has the same thermal conductivity as air. (b)
immediately, leaving the remainder to come to a common temperature
What food intake will the animal need in one day to replace this heat
with the pan?
transfer?
28. In some countries, liquid nitrogen is used on dairy trucks instead of
37. A walrus transfers energy by conduction through its blubber at the
mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid
rate of 150 W when immersed in −1.00ºC water. The walrus’s internal
nitrogen, which has a density of 808 kg/m3 .
core temperature is 37.0ºC , and it has a surface area of 2.00 m2 .
CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 501
What is the average thickness of its blubber, which has the conductivity
45. At what wind speed does −10ºC air cause the same chill factor as
of fatty tissues without blood?
still air at −29ºC ?
46. At what temperature does still air cause the same chill factor as
−5ºC air moving at 15 m/s?
47. 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.
48. (a) How many kilograms of water must evaporate from a 60.0-kg
woman to lower her body temperature by 0.750ºC ?
(b) Is this a reasonable amount of water to evaporate in the form of
perspiration, assuming the relative humidity of the surrounding air is low?
Figure 14.33 Walrus on ice. (credit: Captain Budd Christman, NOAA Corps)
49. On a hot dry day, evaporation from a lake has just enough heat
38. Compare the rate of heat conduction through a 13.0-cm-thick wall
transfer to balance the 1.00 kW/m2 of incoming heat from the Sun.
that has an area of 10.0 m2 and a thermal conductivity twice that of
What mass of water evaporates in 1.00 h from each square meter?
glass wool with the rate of heat conduction through a window that is
Explicitly show how you follow the steps in the Problem-Solving
0.750 cm thick and that has an area of 2.00 m2 , assuming the same
Strategies for the Effects of Heat Transfer.
temperature difference across each.
50. One winter day, the climate control system of a large university
39. Suppose a person is covered head to foot by wool clothing with
classroom building malfunctions. As a result, 500 m3 of excess cold air
average thickness of 2.00 cm and is transferring energy by conduction
is brought in each minute. At what rate in kilowatts must heat transfer
through the clothing at the rate of 50.0 W. What is the temperature
occur to warm this air by 10.0ºC (that is, to bring the air to room
difference across the clothing, given the surface area is 1.40 m2 ?
temperature)?
40. Some stove tops are smooth ceramic for easy cleaning. If the
51. The Kilauea volcano in Hawaii is the world’s most active, disgorging
ceramic is 0.600 cm thick and heat conduction occurs through the same
about 5×105 m3 of 1200ºC lava per day. What is the rate of heat
area and at the same rate as computed in Example 14.6, what is the
transfer out of Earth by convection if this lava has a density of
temperature difference across it? Ceramic has the same thermal
conductivity as glass and brick.
2700 kg/m3 and eventually cools to 30ºC ? Assume that the specific
41. One easy way to reduce heating (and cooling) costs is to add extra
heat of lava is the same as that of granite.
insulation in the attic of a house. Suppose the house already had 15 cm
of fiberglass insulation in the attic and in all the exterior surfaces. If you
added an extra 8.0 cm of fiberglass to the attic, then by what percentage
would the heating cost of the house drop? Take the single story house to
be of dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heat
loss through windows and doors.
42. (a) Calculate the rate of heat conduction through a double-paned
window that has a 1.50-m2 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 15.0ºC , while that on the outside is −10.0ºC . (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.)
Figure 14.34 Lava flow on Kilauea volcano in Hawaii. (credit: J. P. Eaton, U.S.
(b) Calculate the rate of heat conduction through a 1.60-cm-thick window
Geological Survey)
of the same area and with the same temperatures. Compare your answer 52. During heavy exercise, the body pumps 2.00 L of blood per minute to
with that for part (a).
the surface, where it is cooled by 2.00ºC . What is the rate of heat
43. Many decisions are made on the basis of the payback period: the
transfer from this forced convection alone, assuming blood has the same
time it will take through savings to equal the capital cost of an investment.
Acceptable payback times depend upon the business or philosophy one
specific heat as water and its density is 1050 kg/m3 ?
has. (For some industries, a payback period is as small as two years.)
Suppose you wish to install the extra insulation in previous problem. If
53. A person inhales and exhales 2.00 L of 37.0ºC air, evaporating
energy cost $1.00 per million joules and the insulation was $4.00 per
4.00×10−2 g of water from the lungs and breathing passages with
square meter, then calculate the simple payback time. Take the average
Δ T for the 120 day heating season to be 15.0ºC .
each breath.
(a) How much heat transfer occurs due to evaporation in each breath?
44. For the human body, what is the rate of heat transfer by conduction
through the body’s tissue with the following conditions: the tissue
(b) What is the rate of heat transfer in watts if the person is breathing at a
thickness is 3.00 cm, the change in temperature is 2.00ºC , and the skin moderate rate of 18.0 breaths per minute?
area is 1.50 m2 . How does this compare with the average heat transfer (c) If the inhaled air had a temperature of 20.0ºC , what is the rate of
rate to the body resulting from an energy intake of about 2400 kcal per
heat transfer for warming the air?
day? (No exercise is included.)
(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?
502 CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS
54. A glass coffee pot has a circular bottom with a 9.00-cm diameter in
contact with a heating element that keeps the coffee warm with a
continuous heat transfer rate of 50.0 W
(a) What is the temperature of the bottom of the pot, if it is 3.00 mm thick
and the inside temperature is 60.0ºC ?
(b) If the temperature of the coffee remains constant and all of the heat
transfer is removed by evaporation, how many grams per minute
evaporate? Take the heat of vaporization to be 2340 kJ/kg.
55. At what net rate does heat radiate from a 275-m2 black roof on a
night when the roof’s temperature is 30.0ºC and the surrounding
temperature is 15.0ºC ? The emissivity of the roof is 0.900.
56. (a) Cherry-red embers in a fireplace are at 850ºC and have an
Figure 14.35 Artist’s rendition of a thermograph of a patient’s upper body, showing
the distribution of heat represented by different colors.
exposed area of 0.200 m2 and an emissivity of 0.980. The surrounding 62. The Sun radiates like a perfect black body with an emissivity of
room has a temperature of 18.0ºC . If 50% of the radiant energy enters
exactly 1. (a) Calculate the surface temperature of the Sun, given that it
the room, what is the net rate of radiant heat transfer in kilowatts? (b)
is a sphere with a 7.00×108-m radius that radiates 3.80×1026 W
Does your answer support the contention that most of the heat transfer
into 3-K space. (b) How much power does the Sun radiate per square
into a room by a fireplace comes from infrared radiation?
meter of its surface? (c) How much power in watts per square meter is
57. Radiation makes it impossible to stand close to a hot lava flow.
that value at the distance of Earth, 1.50×1011 m away? (This number
Calculate the rate of heat transfer by radiation from 1.00 m2 of
is called the solar constant.)
1200ºC fresh lava into 30.0ºC surroundings, assuming lava’s
63. A large body of lava from a volcano has stopped flowing and is slowly
emissivity is 1.00.
cooling. The interior of the lava is at 1200ºC , its surface is at 450ºC ,
58. (a) Calculate the rate of heat transfer by radiation from a car radiator
and the surroundings are at 27.0ºC . (a) Calculate the rate at which
at 110 ° C into a 50.0ºC environment, if the radiator has an emissivity
energy is transferred by radiation from 1.00 m2 of surface lava into the
of 0.750 and a 1.20-m2 surface area. (b) Is this a significant fraction of
surroundings, assuming the emissivity is 1.00. (b) Suppose heat
the heat transfer by an automobile engine? To answer this, assume a
conduction to the surface occurs at the same rate. What is the thickness
horsepower of 200 hp (1.5 kW) and the efficiency of automobile
of the lava between the 450ºC surface and the 1200ºC interior,
engines as 25%.
assuming that the lava’s conductivity is the same as that of brick?
59. Find the net rate of heat transfer by radiation from a skier standing in
64. Calculate the temperature the entire sky would have to be in order to
the shade, given the following. She is completely clothed in white (head
transfer energy by radiation at 1000 W/m2 —about the rate at which
to foot, including a ski mask), the clothes have an emissivity of 0.200 and
the Sun radiates when it is directly overhead on a clear day. This value is
a surface temperature of 10.0ºC , the surroundings are at −15.0ºC ,
the effective temperature of the sky, a kind of average that takes account
and her surface area is 1.60 m2 .
of the fact that the Sun occupies only a small part of the sky but is much
hotter than the rest. Assume that the body receiving the energy has a
60. Suppose you walk into a sauna that has an ambient temperature of
temperature of 27.0ºC .
50.0ºC . (a) Calculate the rate of heat transfer to you by radiation given 65. (a) A shirtless rider under a circus tent feels the heat radiating from
your skin temperature is 37.0ºC , the emissivity of skin is 0.98, and the
the sunlit portion of the tent. Calculate the temperature of the tent canvas
surface area of your body is 1.50 m2 . (b) If all other forms of heat
based on the following information: The shirtless rider’s skin temperature
transfer are balanced (the net heat transfer is zero), at what rate will your
is 34.0ºC and has an emissivity of 0.970. The exposed area of skin is
body temperature increase if your mass is 75.0 kg?
0.400 m2 . He receives radiation at the rate of 20.0 W—half what you
61. Thermography is a technique for measuring radiant heat and
would calculate if the entire region behind him was hot. The rest of the
detecting variations in surface temperatures that may be medically,
surroundings are at 34.0ºC . (b) Discuss how this situation would
environmentally, or militarily meaningful.(a) What is the percent increase
change if the sunlit side of the tent was nearly pure white and if the rider
in the rate of heat transfer by radiation from a given area at a
was covered by a white tunic.
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
66. Integrated Concepts
transfer by radiation from a given area at a temperature of 34.0ºC
One 30.0ºC day the relative humidity is 75.0% , and that evening the
compared with that at 20.0ºC , such as for warm and cool automobile
temperature drops to 20.0ºC , well below the dew point. (a) How many
hoods?
grams of water condense from each cubic meter of air? (b) How much
heat transfer occurs by this condensation? (c) What temperature
increase could this cause in dry air?
67. 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
109 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
CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS 503
of the meteor is more likely to be deposited in the ocean and the likely
transferred as heat to the body? (b) What is unreasonable about this
effects of that energy.
result? (c) Which premise or assumption is responsible?
68. Integrated Concepts
77. Unreasonable Results
Frozen waste from airplane toilets has sometimes been accidentally
A slightly deranged Arctic inventor surrounded by ice thinks it would be
ejected at high altitude. Ordinarily it breaks up and disperses over a large
much less mechanically complex to cool a car engine by melting ice on it
area, but sometimes it holds together and strikes the ground. Calculate
than by having a water-cooled system with a radiator, water pump,
the mass of 0ºC ice that can be melted by the conversion of kinetic and
antifreeze, and so on. (a) If 80.0% of the energy in 1.00 gal of gasoline
gravitational potential energy when a 20.0 kg piece of frozen waste is
is converted into “waste heat” in a car engine, how many kilograms of
released at 12.0 km altitude while moving at 250 m/s and strikes the
0ºC ice could it melt? (b) Is this a reasonable amount of ice to carry
ground at 100 m/s (since less than 20.0 kg melts, a significant mess
around to cool the engine for 1.00 gal of gasoline consumption? (c) What
results).
premises or assumptions are unreasonable?
69. Integrated Concepts
78. Unreasonable Results
(a) A large electrical power facility produces 1600 MW of “waste heat,”
(a) Calculate the rate of heat transfer by conduction through a window
which is dissipated to the environment in cooling towers by warming air
with an area of 1.00 m2 that is 0.750 cm thick, if its inner surface is at
flowing through the towers by 5.00ºC . What is the necessary flow rate
22.0ºC and its outer surface is at 35.0ºC . (b) What is unreasonable
of air in m3 /s ? (b) Is your result consistent with the large cooling towers about this result? (c) Which premise or assumption is responsible?
used by many large electrical power plants?
79. Unreasonable Results
70. Integrated Concepts
A meteorite 1.20 cm in diameter is so hot immediately after penetrating
(a) Suppose you start a workout on a Stairmaster, producing power at the the atmosphere that it radiates 20.0 kW of power. (a) What is its
same rate as climbing 116 stairs per minute. Assuming your mass is 76.0
temperature, if the surroundings are at 20.0ºC and it has an emissivity
kg and your efficiency is 20.0% , how long will it take for your body
of 0.800? (b) What is unreasonable about this result? (c) Which premise
temperature to rise 1.00ºC if all other forms of heat transfer in and out
or assumption is responsible?
of your body are balanced? (b) Is this consistent with your experience in
80. Construct Your Own Problem
getting warm while exercising?
Consider a new model of commercial airplane having its brakes tested as
71. Integrated Concepts
a part of the initial flight permission procedure. The airplane is brought to
takeoff speed and then stopped with the brakes alone. Construct a
A 76.0-kg person suffering from hypothermia comes indoors and shivers
problem in which you calculate the temperature increase of the brakes
vigorously. How long does it take the heat transfer to increase the
during this process. You may assume most of the kinetic energy of the
person’s body temperature by 2.00ºC if all other forms of heat transfer
airplane is converted to thermal energy in the brakes and surrounding
are balanced?
materials, and that little escapes. Note that the brakes are expected to
72. Integrated Concepts
become so hot in this procedure that they ignite and, in order to pass the
test, the airplane must be able to withstand the fire for some time without
In certain large geographic regions, the underlying rock is hot. Wells can
a general conflagration.
be drilled and water circulated through the rock for heat transfer for the
generation of electricity. (a) Calculate the heat transfer that can be
81. Construct Your Own Problem
extracted by cooling 1.00 km3 of granite by 100ºC . (b) How long will
Consider a person outdoors on a cold night. Construct a problem in
which you calculate the rate of heat transfer from the person by all three
it take for heat transfer at the rate of 300 MW, assuming no heat transfers heat transfer methods. Make the initial circumstances such that at rest
back into the 1.00 km3 of rock by its surroundings?
the person will have a net heat transfer and then decide how much
physical activity of a chosen type is necessary to balance the rate of heat
73. Integrated Concepts
transfer. Among the things to consider are the size of the person, type of
Heat transfers from your lungs and breathing passages by evaporating
clothing, initial metabolic rate, sky conditions, amount of water
water. (a) Calculate the maximum number of grams of water that can be
evaporated, and volume of air breathed. Of course, there are many other
evaporated when you inhale 1.50 L of 37ºC air with an original relative
factors to consider and your instructor may wish to guide you in the
humidity of 40.0%. (Assume that body temperature is also 37ºC .) (b)
assumptions made as well as the detail of analysis and method of
presenting your results.
How many joules of energy are required to evaporate this amount? (c)