Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

while exchanging heat with a single reservoir—a violation of the Kelvin–
Planck statement of the second law. Therefore, our initial assumption that
hth,irrevhth,revis incorrect. Then we conclude that no heat engine can be
more efficient than a reversible heat engine operating between the same
reservoirs.
The second Carnot principle can also be proved in a similar manner. This
time, let us replace the irreversible engine by another reversible engine that
is more efficient and thus delivers more work than the first reversible
engine. By following through the same reasoning, we end up having an
engine that produces a net amount of work while exchanging heat with a
single reservoir, which is a violation of the second law. Therefore, we con-
clude that no reversible heat engine can be more efficient than a reversible
one operating between the same two reservoirs, regardless of how the cycle
is completed or the kind of working fluid used.

6–9 ■ THE THERMODYNAMIC

TEMPERATURE SCALE

A temperature scale that is independent of the properties of the substances
that are used to measure temperature is called a thermodynamic tempera-
ture scale.Such a temperature scale offers great conveniences in thermody-
namic calculations, and its derivation is given below using some reversible
heat engines.
The second Carnot principle discussed in Section 6–8 states that all
reversible heat engines have the same thermal efficiency when operating
between the same two reservoirs (Fig. 6–42). That is, the efficiency of a
reversible engine is independent of the working fluid employed and its
properties, the way the cycle is executed, or the type of reversible engine
used. Since energy reservoirs are characterized by their temperatures, the
thermal efficiency of reversible heat engines is a function of the reservoir
temperatures only. That is,

or

(6–13)

since hth 1 QL/QH. In these relations THand TLare the temperatures of
the high- and low-temperature reservoirs, respectively.
The functional form of f(TH,TL) can be developed with the help of the
three reversible heat engines shown in Fig. 6–43. Engines A and C are sup-
plied with the same amount of heat Q 1 from the high-temperature reservoir
at T 1. Engine C rejects Q 3 to the low-temperature reservoir at T 3. Engine B
receives the heat Q 2 rejected by engine A at temperature T 2 and rejects heat
in the amount of Q 3 to a reservoir at T 3.
The amounts of heat rejected by engines B and C must be the same since
engines A and B can be combined into one reversible engine operating
between the same reservoirs as engine C and thus the combined engine will

QH

QL

f 1 TH, TL 2

hth,revg 1 TH, TL 2

Chapter 6 | 303

Low-temperature reservoir

at TL = 300 K

High-temperature reservoir

at TH = 1000 K

A reversible

HE

ηth,A

η th, A = ηth,B = 70%

Another

reversible

HE

ηth,B

FIGURE 6–42

All reversible heat engines operating

between the same two reservoirs have

the same efficiency (the second Carnot

principle).

WA

Thermal energy reservoir

at T 1

Rev. HE

A

Thermal energy reservoir

at T 3

Rev. HE

B

Q 1

Q 2

Q 2

Q 3

T 2

WB

WC

Rev. HE

C

Q 1

Q 3

FIGURE 6–43

The arrangement of heat engines used

to develop the thermodynamic

temperature scale.

SEE TUTORIAL CH. 6, SEC. 9 ON THE DVD.

INTERACTIVE

TUTORIAL