Physics For Scientists And Engineers 6E - part 152

ntil about 1850, the fields of thermodynamics and mechanics were considered to be

two distinct branches of science, and the law of conservation of energy seemed to de-
scribe only certain kinds of mechanical systems. However, mid-nineteenth-century ex-
periments performed by the Englishman James Joule and others showed that there was
a strong connection between the transfer of energy by heat in thermal processes and
the transfer of energy by work in mechanical processes. Today we know that internal
energy, which we formally define in this chapter, can be transformed to mechanical en-
ergy. Once the concept of energy was generalized from mechanics to include internal
energy, the law of conservation of energy emerged as a universal law of nature.

This chapter focuses on the concept of internal energy, the processes by which en-

ergy is transferred, the first law of thermodynamics, and some of the important appli-
cations of the first law. The first law of thermodynamics is a statement of conservation
of energy. It describes systems in which the only energy change is that of internal en-
ergy and the transfers of energy are by heat and work. Furthermore, the first law makes
no distinction between the results of heat and the results of work. According to the
first law, a system’s internal energy can be changed by an energy transfer to or from the
system either by heat or by work. A major difference in our discussion of work in this
chapter from that in the chapters on mechanics is that we will consider work done on
deformable systems.

20.1 Heat and Internal Energy

At the outset, it is important that we make a major distinction between internal energy
and heat.

Internal energy is all the energy of a system that is associated with its

microscopic components—atoms and molecules—when viewed from a reference
frame at rest with respect to the center of mass of the system. The last part of this
sentence ensures that any bulk kinetic energy of the system due to its motion through
space is not included in internal energy. Internal energy includes kinetic energy of ran-
dom translational, rotational, and vibrational motion of molecules, potential energy
within molecules, and potential energy between molecules. It is useful to relate inter-
nal energy to the temperature of an object, but this relationship is limited—we show in
Section 20.3 that internal energy changes can also occur in the absence of temperature
changes.

Heat is defined as the transfer of energy across the boundary of a system

due to a temperature difference between the system and its surroundings. When
you heat a substance, you are transferring energy into it by placing it in contact with
surroundings that have a higher temperature. This is the case, for example, when you
place a pan of cold water on a stove burner—the burner is at a higher temperature
than the water, and so the water gains energy. We shall also use the term heat to repre-
sent the amount of energy transferred by this method.

Scientists used to think of heat as a fluid called caloric, which they believed was

transferred between objects; thus, they defined heat in terms of the temperature

605

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PITFALL PREVENTION

20.1 Internal Energy,

Thermal Energy, and
Bond Energy

In  reading  other  physics  books,
you may see terms such as thermal
energy and  bond  energy.  Thermal
energy can be interpreted as that
part of the internal energy associ-
ated with random motion of mol-
ecules  and,  therefore,  related  to
temperature.  Bond  energy  is  the
intermolecular  potential  energy.
Thus,

internal energy ! thermal energy

bond energy

While this breakdown is pre-
sented here for clarification with
regard to other texts, we will not
use these terms, because there is
no need for them.

James Prescott Joule

British physicist (1818–1889)

Joule received some formal

education in mathematics,

philosophy, and chemistry from

John Dalton but was in large part

self-educated. Joule’s research

led to the establishment of the

principle of conservation of

energy. His study of the

quantitative relationship among

electrical, mechanical, and

chemical effects of heat

culminated in his announcement

in 1843 of the amount of work

required to produce a unit of

energy, called the mechanical

equivalent of heat. (By kind
permission of the President and
Council of the Royal Society)

changes produced in an object during heating. Today we recognize the distinct differ-
ence between internal energy and heat. Nevertheless, we refer to quantities using
names that do not quite correctly define the quantities but which have become en-
trenched in physics tradition based on these early ideas. Examples of such quantities
are heat capacity and latent heat (Sections 20.2 and 20.3).

As an analogy to the distinction between heat and internal energy, consider the dis-

tinction between work and mechanical energy discussed in Chapter 7. The work done
on a system is a measure of the amount of energy transferred to the system from its sur-
roundings, whereas the mechanical energy of the system (kinetic plus potential) is a
consequence of the motion and configuration of the system. Thus, when a person does
work on a system, energy is transferred from the person to the system. It makes no
sense to talk about the work of a system—one can refer only to the work done on or by a
system when some process has occurred in which energy has been transferred to or
from the system. Likewise, it makes no sense to talk about the heat of a system—one
can refer to heat only when energy has been transferred as a result of a temperature dif-
ference. Both heat and work are ways of changing the energy of a system.

It is also important to recognize that the internal energy of a system can be

changed even when no energy is transferred by heat. For example, when a gas in an
insulated container is compressed by a piston, the temperature of the gas and its in-
ternal energy increase, but no transfer of energy by heat from the surroundings to the
gas has occurred. If the gas then expands rapidly, it cools and its internal energy de-
creases, but no transfer of energy by heat from it to the surroundings has taken place.
The temperature changes in the gas are due not to a difference in temperature be-
tween the gas and its surroundings but rather to the compression and the expansion.
In each case, energy is transferred to or from the gas by work. The changes in internal
energy in these examples are evidenced by corresponding changes in the temperature
of the gas.

Units of Heat

As we have mentioned, early studies of heat focused on the resultant increase in tem-
perature of a substance, which was often water. The early notions of heat based on
caloric suggested that the flow of this fluid from one substance to another caused
changes in temperature. From the name of this mythical fluid, we have an energy
unit related to thermal processes, the

calorie (cal), which is defined as the amount

of energy transfer necessary to raise the temperature of 1 g of water from
14.5°C to 15.5°C.

(Note that the “Calorie,” written with a capital “C” and used in

describing the energy content of foods, is actually a kilocalorie.) The unit of energy
in the U.S. customary system is the

British thermal unit (Btu), which is defined

the amount of energy transfer required to raise the temperature of 1 lb of

water from 63°F to 64°F.

Scientists are increasingly using the SI unit of energy, the joule, when describing ther-

mal processes. In this textbook, heat, work, and internal energy are usually measured in
joules. (Note that both heat and work are measured in energy units. Do not confuse
these two means of energy transfer with energy itself, which is also measured in joules.)

The Mechanical Equivalent of Heat

In Chapters 7 and 8, we found that whenever friction is present in a mechanical sys-
tem, some mechanical energy is lost—in other words, mechanical energy is not con-
served in the presence of nonconservative forces. Various experiments show that this
lost mechanical energy does not simply disappear but is transformed into internal

606

C H A P T E R 2 0 • Heat and the First Law of Thermodynamics

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PITFALL PREVENTION

20.2 Heat, Temperature,

and Internal Energy
Are Different

As you read the newspaper or lis-
ten  to  the  radio,  be  alert  for  in-
correctly  used  phrases  including
the  word  heat, and  think  about
the  proper  word  to  be  used  in
place of heat. Incorrect examples
include “As the truck braked to a
stop,  a  large  amount  of  heat  was
generated  by  friction”  and  “The
heat of a hot summer day . . .”

Originally, the calorie was defined as the “heat” necessary to raise the temperature of 1 g of water

by 1°C. However, careful measurements showed that the amount of energy required to produce a 1°C
change depends somewhat on the initial temperature; hence, a more precise definition evolved.

energy. We can perform such an experiment at home by simply hammering a nail into
a scrap piece of wood. What happens to all the kinetic energy of the hammer once we
have finished? Some of it is now in the nail as internal energy, as demonstrated by the
fact that the nail is measurably warmer. Although this connection between mechanical
and internal energy was first suggested by Benjamin Thompson, it was Joule who estab-
lished the equivalence of these two forms of energy.

A schematic diagram of Joule’s most famous experiment is shown in Figure 20.1.

The system of interest is the water in a thermally insulated container. Work is done on
the water by a rotating paddle wheel, which is driven by heavy blocks falling at a con-
stant speed. The temperature of the stirred water increases due to the friction between
it and the paddles. If the energy lost in the bearings and through the walls is neglected,
then the loss in potential energy associated with the blocks equals the work done by
the paddle wheel on the water. If the two blocks fall through a distance h, the loss in
potential  energy  is  2mgh,  where  m is  the  mass  of  one  block;  this  energy  causes  the
temperature  of  the  water  to  increase.  By  varying  the  conditions  of  the  experiment,
Joule found that the loss in mechanical energy 2mgh is proportional to the increase in
water  temperature  #T.  The  proportionality  constant  was  found  to  be  approximately
4.18 J/g $ °C. Hence, 4.18 J of mechanical energy raises the temperature of 1 g of water
by 1°C. More precise measurements taken later demonstrated the proportionality to be
4.186 J/g $ °C when the temperature of the water was raised from 14.5°C to 15.5°C. We
adopt this “15-degree calorie” value:

1 cal

! 4.186 J

(20.1)

This equality is known, for purely historical reasons, as the

mechanical equivalent

of heat.

20.2 Specific Heat and Calorimetry

When energy is added to a system and there is no change in the kinetic or potential
energy of the system, the temperature of the system usually rises. (An exception to this
statement is the case in which a system undergoes a change of state—also called a phase
transition—as discussed in the next section.) If the system consists of a sample of a sub-
stance, we find that the quantity of energy required to raise the temperature of a given
mass of the substance by some amount varies from one substance to another. For ex-
ample, the quantity of energy required to raise the temperature of 1 kg of water by 1°C
is 4 186 J, but the quantity of energy required to raise the temperature of 1 kg of

S E C T I O N 2 0 . 2 • Specific Heat and Calorimetry

607

Example 20.1 Losing Weight the Hard Way

A student eats a dinner rated at 2 000 Calories. He wishes to
do an equivalent amount of work in the gymnasium by lift-
ing a 50.0-kg barbell. How many times must he raise the bar-
bell to expend this much energy? Assume that he raises the
barbell 2.00 m each time he lifts it and that he regains no
energy when he lowers the barbell.

Solution Because 1 Calorie ! 1.00 % 10

cal, the total amount

of work required to be done on the barbell–Earth system is
2.00 % 10

cal. Converting this value to joules, we have

W ! (2.00 % 10

cal)(4.186 J/cal) ! 8.37 % 10

The work done in lifting the barbell a distance h is equal to
mgh, and the work done in lifting it n times is nmgh. We
equate this to the total work required:

W ! nmgh ! 8.37 % 10

If the student is in good shape and lifts the barbell once
every 5 s, it will take him about 12 h to perform this feat.
Clearly, it is much easier for this student to lose weight by
dieting.

In reality, the human body is not 100% efficient. Thus,

not all of the energy transformed within the body from the
dinner  transfers  out  of  the  body  by  work  done  on  the  bar-
bell.  Some  of  this  energy  is  used  to  pump  blood  and
perform other  functions  within  the  body.  Thus,  the  2 000
Calories  can  be  worked  off  in  less  time  than  12 h  when
these other energy requirements are included.

8.54 % 10

times

n !

mgh

8.37 % 10

(50.0 kg)(9.80 m/s

)(2.00 m)

Thermal

insulator

Figure 20.1 Joule’s experiment for

determining the mechanical

equivalent of heat. The falling

blocks rotate the paddles, causing

the temperature of the water to

increase.

copper by 1°C is only 387 J. In the discussion that follows, we shall use heat as our ex-
ample of energy transfer, but keep in mind that we could change the temperature of
our system by means of any method of energy transfer.

The

heat capacity C of a particular sample of a substance is defined as the amount

of energy needed to raise the temperature of that sample by 1°C. From this definition,
we see that if energy Q produces a change #T in the temperature of a sample, then

Q ! C #T

(20.2)

The

specific heat c of a substance is the heat capacity per unit mass. Thus, if en-

ergy Q transfers to a sample of a substance with mass m and the temperature of the
sample changes by #T, then the specific heat of the substance is

(20.3)

Specific heat is essentially a measure of how thermally insensitive a substance is to the
addition of energy. The greater a material’s specific heat, the more energy must be
added to a given mass of the material to cause a particular temperature change. Table
20.1 lists representative specific heats.

From this definition, we can relate the energy Q transferred between a sample of

mass m of a material and its surroundings to a temperature change #T as

(20.4)

Q ! mc

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C H A P T E R 2 0 • Heat and the First Law of Thermodynamics

Specific heat

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PITFALL PREVENTION

20.3 An Unfortunate

Choice of
Terminology

The name specific heat is an unfor-
tunate  holdover  from  the  days
when  thermodynamics  and  me-
chanics  developed  separately.  A
better  name  would  be  specific
energy  transfer, but  the  existing
term  is  too  entrenched  to  be
replaced.

Specific Heats of Some Substances at 25°C
and Atmospheric Pressure

Table 20.1

Specific heat c

Substance

J/kg ! °C

cal/g ! °C

Elemental solids

Aluminum

900

0.215

Beryllium

1 830

0.436

Cadmium

230

0.055

Copper

387

0.092 4

Germanium

322

0.077

Gold

129

0.030 8

Iron

448

0.107

Lead

128

0.030 5

Silicon

703

0.168

Silver

234

0.056

Other solids

Brass

380

0.092

Glass

837

0.200

Ice (& 5°C)

2 090

0.50

Marble

860

0.21

Wood

1 700

0.41

Liquids

Alcohol (ethyl)

2 400

0.58

Mercury

140

0.033

Water (15°C)

4 186

1.00

Gas

Steam (100°C)

2 010

0.48

Content .. 150 151 152 153 ..