Physical Chemistry Third Edition

112 3 The Second and Third Laws of Thermodynamics: Entropy

and

ηCarnot

wsurr

q 1



Th−Tc

Th

 1 −

Tc

Th

(3.1-22)

By comparison of Eqs. (3.1-14) and (3.1-22),

θc

θh



Tc

Th

(3.1-23)

The thermodynamic temperature and ideal gas temperature are proportional to each

other and Eq. (3.1-22) can be used for any Carnot engine. We choose the kelvin as the

unit for both scales so that the two scales coincide. We will use the symbolTfrom now

on to stand for the temperature on both the thermodynamic scale and the ideal gas scale.

We call both scales theabsolute temperature scaleor theKelvin temperature scale.

Exercise 3.2

Calculate the efficiency of a Carnot heat engine that represents a steam engine with its boiler at

600.0 K and its exhaust at 373.15 K.

The Carnot heat pump coefficient of performance is now

ηhp

1

ηCarnot



1

1 −Tc/Th

(3.1-24)

If a heat pump functions as a refrigerator (or air conditioner), thecoefficient of perfor-

manceis defined to be the heat removed from the cold reservoir divided by the work

put into the refrigerator:

ηr

q′ 2

wcycle



q′ 2

−q′ 2 −q′ 4

−

q 3

q 1 +q 3

ηr

1

−q 1 /q 3 − 1



1

Th/Tc− 1

(3.1-25)

For Carnot heat pumps the coefficient of performance is always greater than unity, and

for Carnot refrigerators the coefficient of performance exceeds unity ifTh/Tc<2.

EXAMPLE 3.1

Calculate the coefficient of performance of a Carnot heat pump operating between a high

temperature of 70.0◦F and a low temperature of 40.0◦F.

Solution

Tc 273 .15 K+(40◦F− 32 ◦F)

(

5K

9 ◦F

)

 277 .59 K