18.In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf
in Antarctica. It was approximately a rectangle 160 km long, 40.0 km
wide, and 250 m thick.
(a) What is the mass of this iceberg, given that the density of ice is
(b) How much heat transfer (in joules) is needed to melt it?
(c) How many years would it take sunlight alone to melt ice this thick, if
the ice absorbs an average of
, 12.00 h per day?
19.How many grams of coffee must evaporate from 350 g of coffee in a
100-g glass cup to cool the coffee from
? 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.)
20.(a) It is difficult to extinguish a fire on a crude oil tanker, because
each liter of crude oil releases
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
boils, and the resulting steam is raised to
. (b) Discuss
additional complications caused by the fact that crude oil has a smaller
density than water.
21.The energy released from condensation in thunderstorms can be
very large. Calculate the energy released into the atmosphere for a
small storm of radius 1 km, assuming that 1.0 cm of rain is precipitated
uniformly over this area.
22.To help prevent frost damage, 4.00 kg of
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
, and assume that no phase change occurs.
23.A 0.250-kg aluminum bowl holding 0.800 kg of soup at
placed in a freezer. What is the final temperature if 377 kJ of energy is
transferred from the bowl and soup, assuming the soup’s thermal
properties are the same as that of water? Explicitly show how you
follow the steps inProblem-Solving Strategies for the Effects of
24.A 0.0500-kg ice cube at
is placed in 0.400 kg of
water in a very well-insulated container. What is the final temperature?
25.If you pour 0.0100 kg of
water onto a 1.20-kg block of ice
(which is initially at
), what is the final temperature? You may
assume that the water cools so rapidly that effects of the surroundings
26.Indigenous people sometimes cook in watertight baskets by placing
hot rocks into water to bring it to a boil. What mass of
must be placed in 4.00 kg of
water to bring its temperature to
, 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.
27.What would be the final temperature of the pan and water in
Calculating the Final Temperature When Heat Is Transferred
Between Two Bodies: Pouring Cold Water in a Hot Panif 0.260 kg
of water was placed in the pan and 0.0100 kg of the water evaporated
immediately, leaving the remainder to come to a common temperature
with the pan?
28.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
(a) Calculate the heat transfer necessary to evaporate this amount of
liquid nitrogen and raise its temperature to
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
ice with that from evaporating the liquid nitrogen.
29.Some gun fanciers make their own bullets, which involves melting
and casting the lead slugs. How much heat transfer is needed to raise
the temperature and melt 0.500 kg of lead, starting from
30.(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
and their inside surface is at
while their outside surface is at
. (b) How many 1-kW room
heaters would be needed to balance the heat transfer due to
31.The rate of heat conduction out of a window on a winter day is rapid
enough to chill the air next to it. To see just how rapidly the windows
transfer heat by conduction, calculate the rate of conduction in watts
window that is
thick (1/4 in) if the
temperatures of the inner and outer surfaces are
, respectively. This rapid rate will not be maintained—the
inner surface will cool, and even result in frost formation.
32.Calculate the rate of heat conduction out of the human body,
assuming that the core internal temperature is
, the skin
, the thickness of the tissues between averages
, and the surface area is
33.Suppose you stand with one foot on ceramic flooring and one foot
on a wool carpet, making contact over an area of
foot. Both the ceramic and the carpet are 2.00 cm thick and are
on their bottom sides. At what rate must heat transfer occur
from each foot to keep the top of the ceramic and carpet at
34.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?
35.(a) A firewalker runs across a bed of hot coals without sustaining
burns. Calculate the heat transferred by conduction into the sole of one
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
. The area of contact is
temperature of the coals is
, and the time in contact is 1.00 s.
(b) What temperature increase is produced in the
(c) What effect do you think this will have on the tissue, keeping in mind
that a callus is made of dead cells?
36.(a) What is the rate of heat conduction through the 3.00-cm-thick fur
of a large animal having a
surface area? Assume that the
animal’s skin temperature is
, that the air temperature is
, 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
37.A walrus transfers energy by conduction through its blubber at the
rate of 150 W when immersed in
water. The walrus’s internal
core temperature is
, and it has a surface area of
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What is the average thickness of its blubber, which has the conductivity
of fatty tissues without blood?
Figure 14.33Walrus on ice. (credit: Captain Budd Christman, NOAA Corps)
38.Compare the rate of heat conduction through a 13.0-cm-thick wall
that has an area of
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
, assuming the same
temperature difference across each.
39.Suppose a person is covered head to foot by wool clothing with
average thickness of 2.00 cm and is transferring energy by conduction
through the clothing at the rate of 50.0 W. What is the temperature
difference across the clothing, given the surface area is
40.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 inExample 14.6, what is the
temperature difference across it? Ceramic has the same thermal
conductivity as glass and brick.
41.One easy way to reduce heating (and cooling) costs is to add extra
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
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
, while that on the outside is
(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
(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).
43.Many decisions are made on the basis of the payback period: the
time it will take through savings to equal the capital cost of an
investment. Acceptable payback times depend upon the business or
philosophy one has. (For some industries, a payback period is as small
as two years.) Suppose you wish to install the extra insulation in
Exercise 14.41. If energy cost $1.00 per million joules and the
insulation was $4.00 per square meter, then calculate the simple
payback time. Take the average
for the 120 day heating season to
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
thickness is 3.00 cm, the change in temperature is
, and the
skin area is
. 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.)
45.At what wind speed does
air cause the same chill factor as
still air at
46.At what temperature does still air cause the same chill factor as
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
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
(b) Is this a reasonable amount of water to evaporate in the form of
perspiration, assuming the relative humidity of the surrounding air is
49.On a hot dry day, evaporation from a lake has just enough heat
transfer to balance the
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 theProblem-Solving
Strategies for the Effects of Heat Transfer.
50.One winter day, the climate control system of a large university
classroom building malfunctions. As a result,
of excess cold
air is brought in each minute. At what rate in kilowatts must heat
transfer occur to warm this air by
(that is, to bring the air to
51.The Kilauea volcano in Hawaii is the world’s most active, disgorging
lava per day. What is the rate of heat
transfer out of Earth by convection if this lava has a density of
and eventually cools to
? Assume that the specific
heat of lava is the same as that of granite.
Figure 14.34Lava flow on Kilauea volcano in Hawaii. (credit: J. P. Eaton, U.S.
52.During heavy exercise, the body pumps 2.00 L of blood per minute
to the surface, where it is cooled by
. What is the rate of heat
transfer from this forced convection alone, assuming blood has the
same specific heat as water and its density is
53.A person inhales and exhales 2.00 L of
of water from the lungs and breathing passages with
(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?
(c) If the inhaled air had a temperature of
, what is the rate of
heat transfer for warming the air?
CHAPTER 14 | HEAT AND HEAT TRANSFER METHODS S 501
(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
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
(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
black roof on a
night when the roof’s temperature is
and the surrounding
? The emissivity of the roof is 0.900.
56.(a) Cherry-red embers in a fireplace are at
and have an
exposed area of
and an emissivity of 0.980. The
surrounding room has a temperature of
. If 50% of the radiant
energy enters the room, what is the net rate of radiant heat transfer in
kilowatts? (b) Does your answer support the contention that most of the
heat transfer into a room by a fireplace comes from infrared radiation?
57.Radiation makes it impossible to stand close to a hot lava flow.
Calculate the rate of heat transfer by radiation from
fresh lava into
surroundings, assuming lava’s
emissivity is 1.00.
58.(a) Calculate the rate of heat transfer by radiation from a car
environment, if the radiator has an
emissivity of 0.750 and a
surface area. (b) Is this a
significant fraction of the heat transfer by an automobile engine? To
answer this, assume a horsepower of
efficiency of automobile engines as 25%.
59.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
, the surroundings are at
, and her surface area is
60.Suppose you walk into a sauna that has an ambient temperature of
. (a) Calculate the rate of heat transfer to you by radiation
given your skin temperature is
, the emissivity of skin is 0.98,
and the surface area of your body is
. (b) If all other forms of
heat transfer are balanced (the net heat transfer is zero), at what rate
will your body temperature increase if your mass is 75.0 kg?
61.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
compared with that at
, 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
compared with that at
, such as for warm and cool automobile
Figure 14.35Artist’s rendition of a thermograph of a patient’s upper body, showing
the distribution of heat represented by different colors.
62.The Sun radiates like a perfect black body with an emissivity of
exactly 1. (a) Calculate the surface temperature of the Sun, given that it
is a sphere with a
radius that radiates
into 3-K space. (b) How much power does the Sun radiate per square
meter of its surface? (c) How much power in watts per square meter is
that value at the distance of Earth,
away? (This number
is called the solar constant.)
63.A large body of lava from a volcano has stopped flowing and is
slowly cooling. The interior of the lava is at
, its surface is at
, and the surroundings are at
. (a) Calculate the rate at
which energy is transferred by radiation from
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
surface and the
interior, assuming that the lava’s conductivity is the same as that of
64.Calculate the temperature the entire sky would have to be in order
to transfer energy by radiation at
—about the rate at
which the Sun radiates when it is directly overhead on a clear day. This
value is the effective temperature of the sky, a kind of average that
takes account 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 temperature of
65.(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
and has an emissivity of 0.970. The exposed
area of skin is
. 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
. (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.
day the relative humidity is
, and that evening the
temperature drops to
, well below the dew point. (a) How many
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?
Large meteors sometimes strike the Earth, converting most of their
kinetic energy into thermal energy. (a) What is the kinetic energy of a
meteor moving at 25.0 km/s? (b) If this meteor lands in a deep
of its kinetic energy goes into heating water, how
many kilograms of water could it raise by
(c) Discuss how the
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energy of the meteor is more likely to be deposited in the ocean and the
likely effects of that energy.
Frozen waste from airplane toilets has sometimes been accidentally
ejected at high altitude. Ordinarily it breaks up and disperses over a
large area, but sometimes it holds together and strikes the ground.
Calculate the mass of
ice that can be melted by the conversion of
kinetic and gravitational potential energy when a
frozen waste is released at 12.0 km altitude while moving at 250 m/s
and strikes the ground at 100 m/s (since less than 20.0 kg melts, a
significant mess results).
(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
. What is the necessary flow rate
of air in
? (b) Is your result consistent with the large cooling
towers used by many large electrical power plants?
(a) Suppose you start a workout on a Stairmaster, producing power at
the same rate as climbing 116 stairs per minute. Assuming your mass is
76.0 kg and your efficiency is
, how long will it take for your
body temperature to rise
if all other forms of heat transfer in
and out of your body are balanced? (b) Is this consistent with your
experience in getting warm while exercising?
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
if all other forms of heat
transfer are balanced?
In certain large geographic regions, the underlying rock is hot. Wells
can be drilled and water circulated through the rock for heat transfer for
the generation of electricity. (a) Calculate the heat transfer that can be
extracted by cooling
of granite by
. (b) How long
will it take for heat transfer at the rate of 300 MW, assuming no heat
transfers back into the
of rock by its surroundings?
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
air with an original relative
humidity of 40.0%. (Assume that body temperature is also
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?
(a) What is the temperature increase of water falling 55.0 m over
Niagara Falls? (b) What fraction must evaporate to keep the
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
air. (b) What energy is needed to cause
of air to go from
? (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?
(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?
A slightly deranged Arctic inventor surrounded by ice thinks it would be
much less mechanically complex to cool a car engine by melting ice on
it than by having a water-cooled system with a radiator, water pump,
antifreeze, and so on. (a) If
of the energy in 1.00 gal of
gasoline is converted into “waste heat” in a car engine, how many
ice could it melt? (b) Is this a reasonable amount of
ice to carry around to cool the engine for 1.00 gal of gasoline
consumption? (c) What premises or assumptions are unreasonable?
(a) Calculate the rate of heat transfer by conduction through a window
with an area of
that is 0.750 cm thick, if its inner surface is at
and its outer surface is at
. (b) What is unreasonable
about this result? (c) Which premise or assumption is responsible?
A meteorite 1.20 cm in diameter is so hot immediately after penetrating
the atmosphere that it radiates 20.0 kW of power. (a) What is its
temperature, if the surroundings are at
and it has an emissivity
of 0.800? (b) What is unreasonable about this result? (c) Which
premise or assumption is responsible?
80.Construct Your Own Problem
Consider a new model of commercial airplane having its brakes tested
as a part of the initial flight permission procedure. The airplane is
brought to takeoff speed and then stopped with the brakes alone.
Construct a problem in which you calculate the temperature increase of
the brakes during this process. You may assume most of the kinetic
energy of the airplane is converted to thermal energy in the brakes and
surrounding materials, and that little escapes. Note that the brakes are
expected to 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 a general conflagration.
81.Construct Your Own Problem
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
heat transfer methods. Make the initial circumstances such that at rest
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 transfer. Among the things to consider are the size of the person,
type of clothing, initial metabolic rate, sky conditions, amount of water
evaporated, and volume of air breathed. Of course, there are many
other factors to consider and your instructor may wish to guide you in
the assumptions made as well as the detail of analysis and method of
presenting your results.
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Figure 15.1A steam engine uses heat transfer to do work. Tourists regularly ride this narrow-gauge steam engine train near the San Juan Skyway in Durango, Colorado, part
of the National Scenic Byways Program. (credit: Dennis Adams)
15.1.The First Law of Thermodynamics
• Define the first law of thermodynamics.
• Describe how conservation of energy relates to the first law of thermodynamics.
• Identify instances of the first law of thermodynamics working in everyday situations, including biological metabolism.
• Calculate changes in the internal energy of a system, after accounting for heat transfer and work done.
15.2.The First Law of Thermodynamics and Some Simple Processes
• Describe the processes of a simple heat engine.
• Explain the differences among the simple thermodynamic processes—isobaric, isochoric, isothermal, and adiabatic.
• Calculate total work done in a cyclical thermodynamic process.
15.3.Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency
• State the expressions of the second law of thermodynamics.
• Calculate the efficiency and carbon dioxide emission of a coal-fired electricity plant, using second law characteristics.
• Describe and define the Otto cycle.
15.4.Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated
• Identify a Carnot cycle.
• Calculate maximum theoretical efficiency of a nuclear reactor.
• Explain how dissipative processes affect the ideal Carnot engine.
15.5.Applications of Thermodynamics: Heat Pumps and Refrigerators
• Describe the use of heat engines in heat pumps and refrigerators.
• Demonstrate how a heat pump works to warm an interior space.
• Explain the differences between heat pumps and refrigerators.
• Calculate a heat pump’s coefficient of performance.
15.6.Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy
• Define entropy.
• Calculate the increase of entropy in a system with reversible and irreversible processes.
• Explain the expected fate of the universe in entropic terms.
• Calculate the increasing disorder of a system.
15.7.Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation
• Identify probabilities in entropy.
• Analyze statistical probabilities in entropic systems.
CHAPTER 15 | THERMODYNAMICS S 505
Introduction to Thermodynamics
Heat transfer is energy in transit, and it can be used to do work. It can also be converted to any other form of energy. A car engine, for example,
burns fuel for heat transfer into a gas. Work is done by the gas as it exerts a force through a distance, converting its energy into a variety of other
forms—into the car’s kinetic or gravitational potential energy; into electrical energy to run the spark plugs, radio, and lights; and back into stored
energy in the car’s battery. But most of the heat transfer produced from burning fuel in the engine does not do work on the gas. Rather, the energy is
released into the environment, implying that the engine is quite inefficient.
It is often said that modern gasoline engines cannot be made to be significantly more efficient. We hear the same about heat transfer to electrical
energy in large power stations, whether they are coal, oil, natural gas, or nuclear powered. Why is that the case? Is the inefficiency caused by design
problems that could be solved with better engineering and superior materials? Is it part of some money-making conspiracy by those who sell energy?
Actually, the truth is more interesting, and reveals much about the nature of heat transfer.
Basic physical laws govern how heat transfer for doing work takes place and place insurmountable limits onto its efficiency. This chapter will explore
these laws as well as many applications and concepts associated with them. These topics are part ofthermodynamics—the study of heat transfer
and its relationship to doing work.
15.1The First Law of Thermodynamics
Figure 15.2This boiling tea kettle represents energy in motion. The water in the kettle is turning to water vapor because heat is being transferred from the stove to the kettle.
As the entire system gets hotter, work is done—from the evaporation of the water to the whistling of the kettle. (credit: Gina Hamilton)
If we are interested in how heat transfer is converted into doing work, then the conservation of energy principle is important. The first law of
thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy
into and out of the system. Thefirst law of thermodynamicsstates that the change in internal energy of a system equals the net heat transferinto
the system minus the net work donebythe system. In equation form, the first law of thermodynamics is
is thechange in internal energy
of the system.
is thenet heat transferred into the system—that is,
is the sum of all heat
transfer into and out of the system.
is thenet work done by the system—that is,
is the sum of all work done on or by the system. We use the
following sign conventions: if
is positive, then there is a net heat transfer into the system; if
is positive, then there is net work done by the
system. So positive
adds energy to the system and positive
takes energy from the system. Thus
. Note also that if more heat
transfer into the system occurs than work done, the difference is stored as internal energy. Heat engines are a good example of this—heat transfer
into them takes place so that they can do work. (SeeFigure 15.3.) We will now examine
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Figure 15.3The first law of thermodynamics is the conservation-of-energy principle stated for a system where heat and work are the methods of transferring energy for a
system in thermal equilibrium.
represents the net heat transfer—it is the sum of all heat transfers into and out of the system.
is positive for net heat transferintothe
is the total work done on and by the system.
is positive when more work is donebythe system than on it. The change in the internal energy of the system,
, is related to heat and work by the first law of thermodynamics,
Making Connections: Law of Thermodynamics and Law of Conservation of Energy
The first law of thermodynamics is actually the law of conservation of energy stated in a form most useful in thermodynamics. The first law gives
the relationship between heat transfer, work done, and the change in internal energy of a system.
Heat transfer (
) and doing work (
) are the two everyday means of bringing energy into or taking energy out of a system. The processes are
quite different. Heat transfer, a less organized process, is driven by temperature differences. Work, a quite organized process, involves a
macroscopic force exerted through a distance. Nevertheless, heat and work can produce identical results.For example, both can cause a temperature
increase. Heat transfer into a system, such as when the Sun warms the air in a bicycle tire, can increase its temperature, and so can work done on
the system, as when the bicyclist pumps air into the tire. Once the temperature increase has occurred, it is impossible to tell whether it was caused by
heat transfer or by doing work. This uncertainty is an important point. Heat transfer and work are both energy in transit—neither is stored as such in a
system. However, both can change the internal energy
of a system. Internal energy is a form of energy completely different from either heat or
We can think about the internal energy of a system in two different but consistent ways. The first is the atomic and molecular view, which examines
the system on the atomic and molecular scale. Theinternal energy
of a system is the sum of the kinetic and potential energies of its atoms and
molecules. Recall that kinetic plus potential energy is called mechanical energy. Thus internal energy is the sum of atomic and molecular mechanical
energy. Because it is impossible to keep track of all individual atoms and molecules, we must deal with averages and distributions. A second way to
view the internal energy of a system is in terms of its macroscopic characteristics, which are very similar to atomic and molecular average values.
Macroscopically, we define the change in internal energy
to be that given by the first law of thermodynamics:
Many detailed experiments have verified that
is the change in total kinetic and potential energy of all atoms and
molecules in a system. It has also been determined experimentally that the internal energy
of a system depends only on the state of the system
andnot how it reached that state.More specifically,
is found to be a function of a few macroscopic quantities (pressure, volume, and temperature,
for example), independent of past history such as whether there has been heat transfer or work done. This independence means that if we know the
state of a system, we can calculate changes in its internal energy
from a few macroscopic variables.
Making Connections: Macroscopic and Microscopic
In thermodynamics, we often use the macroscopic picture when making calculations of how a system behaves, while the atomic and molecular
picture gives underlying explanations in terms of averages and distributions. We shall see this again in later sections of this chapter. For
example, in the topic of entropy, calculations will be made using the atomic and molecular view.
To get a better idea of how to think about the internal energy of a system, let us examine a system going from State 1 to State 2. The system has
in State 1, and it has internal energy
in State 2, no matter how it got to either state. So the change in internal energy
is independent of what caused the change. In other words,
is independent of path. By path, we mean the method of getting
from the starting point to the ending point. Why is this independence important? Note that
depend on path, but
does not. This path independence means that internal energy
is easier to consider than either heat transfer or work done.
CHAPTER 15 | THERMODYNAMICS S 507
Example 15.1Calculating Change in Internal Energy: The Same Change in n U is Produced by Two Different
(a) Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the
system while 4.00 J of work is done on the system. What is the net change in internal energy of the system?
(b) What is the change in internal energy of a system when a total of 150.00 J of heat transfer occurs out of (from) the system and 159.00 J of
work is done on the system? (SeeFigure 15.4).
In part (a), we must first find the net heat transfer and net work done from the given information. Then the first law of thermodynamics
can be used to find the change in internal energy. In part (b), the net heat transfer and work done are given, so the equation
can be used directly.
Solution for (a)
The net heat transfer is the heat transfer into the system minus the heat transfer out of the system, or
Q=40.00J −25.00 J=15.00J.
Similarly, the total work is the work done by the system minus the work done on the system, or
W=10.00J −4.00J J =6.00 J.
Thus the change in internal energy is given by the first law of thermodynamics:
ΔU=Q−W=15.00J −6.00J =9.00 J.
We can also find the change in internal energy for each of the two steps. First, consider 40.00 J of heat transfer in and 10.00 J of work out, or
=40.00J −10.00J J =30.00 J.
Now consider 25.00 J of heat transfer out and 4.00 J of work in, or
=-25.00J −(−4.00J)=–21.00 J.
The total change is the sum of these two steps, or
=30.00J +(−21.00J)=9.00 J.
Discussion on (a)
No matter whether you look at the overall process or break it into steps, the change in internal energy is the same.
Solution for (b)
Here the net heat transfer and total work are given directly to be
Q= –150.00 J
W= –159.00 J
, so that
ΔU=Q–W= –150.00 J–(−159.00 J)=9.00 J.
Discussion on (b)
A very different process in part (b) produces the same 9.00-J change in internal energy as in part (a). Note that the change in the system in both
parts is related to
and not to the individual
s involved. The system ends up in thesamestate in both (a) and (b). Parts (a) and
(b) present two different paths for the system to follow between the same starting and ending points, and the change in internal energy for each
is the same—it is independent of path.
508 CHAPTER 15 | THERMODYNAMICS
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