Physics For Scientists And Engineers 6E - part 158

radiate all its energy, and its temperature would reach absolute zero. The energy an
object absorbs comes from its surroundings, which consist of other objects that radi-
ate energy. If an object is at a temperature T and its surroundings are at an average
temperature T

, then the net rate of energy gained or lost by the object as a result of

radiation is

(20.19)

When an object is in equilibrium with its surroundings, it radiates and absorbs

energy at the same rate, and its temperature remains constant. When an object is
hotter than its surroundings, it radiates more energy than it absorbs, and its tempera-
ture decreases.

ideal absorber is defined as an object that absorbs all the energy incident on it,

and for such an object, e ! 1. An object for which e ! 1 is often referred to as a

black

body. We shall investigate experimental and theoretical approaches to radiation from a
black body in Chapter 40. An ideal absorber is also an ideal radiator of energy. In
contrast, an object for which e ! 0 absorbs none of the energy incident on it. Such an
object reflects all the incident energy, and thus is an

ideal reflector.

The Dewar Flask

The Dewar flask

is a container designed to minimize energy losses by conduction, con-

vection, and radiation. Such a container is used to store either cold or hot liquids for
long periods of time. (A Thermos bottle is a common household equivalent of a Dewar
flask.) The standard construction (Fig. 20.16) consists of a double-walled Pyrex glass
vessel with silvered walls. The space between the walls is evacuated to minimize energy
transfer by conduction and convection. The silvered surfaces minimize energy transfer
by radiation because silver is a very good reflector and has very low emissivity. A further
reduction in energy loss is obtained by reducing the size of the neck. Dewar flasks are
commonly used to store liquid nitrogen (boiling point: 77 K) and liquid oxygen (boil-
ing point: 90 K).

To confine liquid helium (boiling point: 4.2 K), which has a very low heat of vapor-

ization, it is often necessary to use a double Dewar system, in which the Dewar flask
containing the liquid is surrounded by a second Dewar flask. The space between the
two flasks is filled with liquid nitrogen.

Newer designs of storage containers use “super insulation” that consists of many

layers of reflecting material separated by fiberglass. All of this is in a vacuum, and no
liquid nitrogen is needed with this design.

net

Ae(T

)

S E C T I O N 2 0 . 7 • Energy Transfer Mechanisms

629

Invented by Sir James Dewar (1842–1923).

Vacuum

Silvered

surfaces

Hot or

cold

liquid

Figure 20.16 A cross-sectional

view of a Dewar flask, which is used

to store hot or cold substances.

Example 20.11 Who Turned Down the Thermostat?

A student is trying to decide what to wear. The surroundings
(his bedroom) are at 20.0°C. If the skin temperature of the
unclothed student is 35°C, what is the net energy loss from
his body in 10.0 min by radiation? Assume that the emissivity
of skin is 0.900 and that the surface area of the student is
1.50 m

Solution Using Equation 20.19, we find that the net rate of
energy loss from the skin is

net

Ae(T

)

At this rate, the total energy lost by the skin in 10 min is

Note that the energy radiated by the student is roughly
equivalent to that produced by two 60-W light bulbs!

7.5 % 10

Q ! !

net

t ! (125 W)(600 s) !

(0.900)[(308 K)

(293 K)

] ! 125 W

(5.67 % 10

W/m

)(1.50 m

)

630

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

Internal energy is all of a system’s energy that is associated with the system’s mi-

croscopic components. Internal energy includes kinetic energy of random translation,
rotation, and vibration of molecules, potential energy within molecules, and potential
energy between molecules.

Heat is the transfer of energy across the boundary of a system resulting from a tem-

perature difference between the system and its surroundings. We use the symbol Q for
the amount of energy transferred by this process.

The

calorie is the amount of energy necessary to raise the temperature of 1 g of

water from 14.5°C to 15.5°C. The

mechanical equivalent of heat is 1 cal ! 4.186 J.

The

heat capacity C of any sample is the amount of energy needed to raise the

temperature of the sample by 1°C. The energy Q required to change the temperature
of a mass m of a substance by an amount #T is

Q ! mc #T

(20.4)

where c is the

specific heat of the substance.

The energy required to change the phase of a pure substance of mass m is

Q ! * mL

(20.6)

where L is the

latent heat of the substance and depends on the nature of the phase

change and the properties of the substance. The positive sign is used if energy is enter-
ing the system, and the negative sign is used if energy is leaving.

The

work done on a gas as its volume changes from some initial value V

to some

final value V

(20.8)

where P is the pressure, which may vary during the process. In order to evaluate W, the
process must be fully specified—that is, P and V must be known during each step. In
other words, the work done depends on the path taken between the initial and final
states.

The

first law of thermodynamics states that when a system undergoes a change

from one state to another, the change in its internal energy is

(20.9)

where Q is the energy transferred into the system by heat and W is the work done on
the system. Although Q and W both depend on the path taken from the initial state to
the final state, the quantity #E

int

is path-independent.

In a

cyclic process (one that originates and terminates at the same state),

int

0 and, therefore, Q ! & W. That is, the energy transferred into the system by

heat equals the negative of the work done on the system during the process.

In an

adiabatic process, no energy is transferred by heat between the system and

its surroundings (Q ! 0). In this case, the first law gives #E

int

W. That is, the inter-

nal energy changes as a consequence of work being done on the system. In the

adia-

batic free expansion of a gas Q ! 0 and W ! 0, and so #E

int

0. That is, the internal

energy of the gas does not change in such a process.

isobaric process is one that occurs at constant pressure. The work done on a

gas in such a process is W ! & P(V

isovolumetric process is one that occurs at constant volume. No work is done

in such a process, so #E

int

isothermal process is one that occurs at constant temperature. The work done

on an ideal gas during an isothermal process is

(20.13)

W ! nRT

int

Q " W

W ! &

S U M M A R Y

Take a practice test for

this chapter by clicking on
the Practice Test link at
http://www.pse6.com.

Questions

631

Energy may be transferred by work, which we addressed in Chapter 7, and by

conduction, convection, or radiation.

Conduction can be viewed as an exchange of

kinetic energy between colliding molecules or electrons. The rate of energy transfer by
conduction through a slab of area A is

(20.14)

where k is the

thermal conductivity of the material from which the slab is made

and

is the

temperature gradient. This equation can be used in many situa-

tions in which the rate of transfer of energy through materials is important.

convection, a warm substance transfers energy from one location to another.

All objects emit

radiation in the form of electromagnetic waves at the rate

! ! /

AeT

(20.18)

An object that is hotter than its surroundings radiates more energy than it absorbs,
whereas an object that is cooler than its surroundings absorbs more energy than it
radiates.

dT/dx&

! !

1. Clearly distinguish among temperature, heat, and internal

energy.

2. Ethyl alcohol has about half the specific heat of water. If

equal-mass samples of alcohol and water in separate
beakers are supplied with the same amount of energy,
compare the temperature increases of the two liquids.

3. A small metal crucible is taken from a 200°C oven and im-

mersed in a tub full of water at room temperature (this
process is often referred to as quenching). What is the ap-
proximate final equilibrium temperature?

4. What is a major problem that arises in measuring specific

heats if a sample with a temperature above 100°C is placed
in water?

5. In a daring lecture demonstration, an instructor dips his wet-

ted  fingers  into  molten  lead  (327°C)  and  withdraws  them
quickly, without getting burned. How is this possible? (This is
a  dangerous  experiment,  which  you  should  NOT attempt.)
What  is  wrong  with  the  following  statement?  “Given  any
two objects, the one with the higher temperature contains
more heat.”

7. Why is a person able to remove a piece of dry aluminum

foil from a hot oven with bare fingers, while a burn results
if there is moisture on the foil?
The air temperature above coastal areas is profoundly influ-
enced by the large specific heat of water. One reason is that
the energy released when 1 m

of water cools by 1°C will

raise the temperature of a much larger volume of air by 1°C.
Find this volume of air. The specific heat of air is approxi-
mately 1 kJ/kg $ °C. Take the density of air to be 1.3 kg/m

9. Concrete has a higher specific heat than soil. Use this fact

to  explain  (partially)  why  cities  have  a  higher  average
nighttime temperature than the surrounding countryside.
If a city is hotter than the surrounding countryside, would
you  expect  breezes  to  blow  from  city  to  country  or  from
country to city? Explain.
Using  the  first  law  of  thermodynamics,  explain  why  the
total energy of an isolated system is always constant.

10.

11. When a sealed Thermos bottle full of hot coffee is shaken,

what are the changes, if any, in (a) the temperature of the
coffee (b) the internal energy of the coffee?

12. Is it possible to convert internal energy to mechanical

energy? Explain with examples.

13. The U.S. penny was formerly made mostly of copper and is

now made of copper-coated zinc. Can a calorimetric exper-
iment be devised to test for the metal content in a collec-
tion of pennies? If so, describe the procedure you would
use.

14. Figure Q20.14 shows a pattern formed by snow on the roof

of a barn. What causes the alternating pattern of snow-
covered and exposed roof ?

15. A tile floor in a bathroom may feel uncomfortably cold to

your bare feet, but a carpeted floor in an adjoining room
at the same temperature will feel warm. Why?

16. Why can potatoes be baked more quickly when a metal

skewer has been inserted through them?

Q U E S T I O N S

Figure Q20.14 Alternating patterns on a snow-covered roof.

Courtesy of Dr

. Albert A. Bartlett, University of Colorado, Boulder

, CO

632

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

17. A piece of paper is wrapped around a rod made half of

wood and half of copper. When held over a flame, the pa-
per in contact with the wood burns but the half in contact
with the metal does not. Explain.

18. Why do heavy draperies over the windows help keep a

home cool in the summer, as well as warm in the winter?

19. If you wish to cook a piece of meat thoroughly on an open

fire, why should you not use a high flame? (Note that car-
bon is a good thermal insulator.)

20. In an experimental house, Styrofoam beads were pumped

into the air space between the panes of glass in double
windows at night in the winter, and pumped out to hold-
ing bins during the day. How would this assist in conserv-
ing energy in the house?

21. Pioneers stored fruits and vegetables in underground cel-

lars. Discuss the advantages of this choice for a storage site.

22. The pioneers referred to in the last question found that a

large tub of water placed in a storage cellar would prevent
their food from freezing on really cold nights. Explain why
this is so.

23. When camping in a canyon on a still night, one notices

that as soon as the sun strikes the surrounding peaks, a
breeze begins to stir. What causes the breeze?

24. Updrafts of air are familiar to all pilots and are used to keep

nonmotorized gliders aloft. What causes these currents?

25. If water is a poor thermal conductor, why can its tempera-

ture be raised quickly when it is placed over a flame?

26. Why is it more comfortable to hold a cup of hot tea by the

handle rather than by wrapping your hands around the
cup itself?

27. If you hold water in a paper cup over a flame, you can

bring the water to a boil without burning the cup. How is
this possible?

28. You need to pick up a very hot cooking pot in your

kitchen. You have a pair of hot pads. Should you soak
them in cold water or keep them dry, to be able to pick up
the pot most comfortably?

29. Suppose you pour hot coffee for your guests, and one of

them wants to drink it with cream, several minutes later,
and then as warm as possible. In order to have the warmest

coffee, should the person add the cream just after the cof-
fee is poured or just before drinking? Explain.

30. Two identical cups both at room temperature are filled

with the same amount of hot coffee. One cup contains a
metal spoon, while the other does not. If you wait for sev-
eral minutes, which of the two will have the warmer cof-
fee? Which energy transfer process explains your answer?

31. A warning sign often seen on highways just before a bridge

is “Caution—Bridge surface freezes before road surface.”
Which of the three energy transfer processes discussed in
Section 20.7 is most important in causing a bridge surface
to freeze before a road surface on very cold days?

32. A professional physics teacher drops one marshmallow into

a flask of liquid nitrogen, waits for the most energetic boil-
ing to stop, fishes it out with tongs, shakes it off, pops it into
his mouth, chews it up, and swallows it. Clouds of ice crystals
issue from his mouth as he crunches noisily and comments
on the sweet taste. How can he do this without injury?
Caution: Liquid nitrogen can be a dangerous substance and
you should not try this yourself. The teacher might be badly
injured if he did not shake it off, if he touched the tongs to
a tooth, or if he did not start with a mouthful of saliva.

33. In 1801 Humphry Davy rubbed together pieces of ice inside

an  ice-house.  He  took  care  that  nothing  in  their  environ-
ment  was  at  a  higher  temperature  than  the  rubbed  pieces.
He observed the production of drops of liquid water. Make a
table listing this and other experiments or processes, to illus-
trate each of the following. (a) A system can absorb energy
by heat, increase in internal energy, and increase in tempera-
ture. (b) A system can absorb energy by heat and increase in
internal  energy,  without  an  increase  in  temperature.  (c)  A
system can absorb energy by heat without increasing in tem-
perature or in internal energy. (d) A system can increase in
internal  energy  and  in  temperature,  without  absorbing  en-
ergy  by  heat.  (e)  A  system  can  increase  in  internal  energy
without absorbing energy by heat or increasing in tempera-
ture.  (f)  What  If ? If  a  system’s  temperature  increases,  is  it
necessarily true that its internal energy increases?

34. Consider the opening photograph for Part 3 on page 578.

Discuss the roles of conduction, convection, and radiation
in the operation of the cooling fins on the support posts of
the Alaskan oil pipeline.

Section 20.1 Heat and Internal Energy

On his honeymoon James Joule traveled from England to
Switzerland. He attempted to verify his idea of the inter-
convertibility of mechanical energy and internal energy by
measuring the increase in temperature of water that fell in
a waterfall. If water at the top of an alpine waterfall has a
temperature of 10.0°C and then falls 50.0 m (as at Niagara

Falls), what maximum temperature at the bottom of the
falls could Joule expect? He did not succeed in measuring
the temperature change, partly because evaporation
cooled the falling water, and also because his thermometer
was not sufficiently sensitive.

Consider Joule’s apparatus described in Figure 20.1. The
mass of each of the two blocks is 1.50 kg, and the insulated

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