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

have the same efficiency as engine C. Since the heat input to engine C is the

same as the heat input to the combined engines A and B, both systems must

reject the same amount of heat.

Applying Eq. 6–13 to all three engines separately, we obtain

Now consider the identity

which corresponds to

A careful examination of this equation reveals that the left-hand side is a

function of T 1 and T 3 , and therefore the right-hand side must also be a func-

tion of T 1 and T 3 only, and not T 2. That is, the value of the product on the

right-hand side of this equation is independent of the value of T 2. This con-

dition will be satisfied only if the function fhas the following form:

so that f(T 2 ) will cancel from the product of f(T 1 ,T 2 ) and f(T 2 ,T 3 ), yielding

(6–14)

This relation is much more specific than Eq. 6–13 for the functional form of

Q 1 /Q 3 in terms of T 1 and T 3.

For a reversible heat engine operating between two reservoirs at tempera-

tures THand TL, Eq. 6–14 can be written as

(6–15)

This is the only requirement that the second law places on the ratio of heat

transfers to and from the reversible heat engines. Several functions f(T) sat-

isfy this equation, and the choice is completely arbitrary. Lord Kelvin first

proposed taking f(T) Tto define a thermodynamic temperature scale as

(Fig. 6–44)

(6–16)

This temperature scale is called the Kelvin scale,and the temperatures on

this scale are called absolute temperatures.On the Kelvin scale, the tem-

perature ratios depend on the ratios of heat transfer between a reversible heat

engine and the reservoirs and are independent of the physical properties of

any substance. On this scale, temperatures vary between zero and infinity.

The thermodynamic temperature scale is not completely defined by

Eq. 6–16 since it gives us only a ratio of absolute temperatures. We also

need to know the magnitude of a kelvin. At the International Conference on

a

QH

QL

b

rev



TH

TL

QH

QL



f 1 TH 2

f 1 TL 2

Q 1

Q 3

f 1 T 1 , T 32 

f 1 T 12

f 1 T 32

f 1 T 1 , T 22 

f 1 T 12

f 1 T 22

¬and¬f 1 T 2 , T 32 

f 1 T 22

f 1 T 32

f 1 T 1 , T 32 f 1 T 1 , T 22 # f 1 T 2 , T 32

Q 1

Q 3



Q 1

Q 2

¬

Q 2

Q 3

Q 1

Q 2

f 1 T 1 , T 22 ,¬

Q 2

Q 3

f 1 T 2 , T 32 ,¬and¬

Q 1

Q 3

f 1 T 1 , T 32

304 | Thermodynamics

Low-temperature reservoir

at TL

High-temperature reservoir

at TH

Reversible

heat engine

or

refrigerator

QH

QL

Wnet

QH

QL

TH

TL

=

FIGURE 6–44

For reversible cycles, the heat transfer
ratio QH/QLcan be replaced by the
absolute temperature ratio TH/TL.