Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics^43

Solution:
The number of moles of lg nitrogen is

n = 1/28 = 3.57 x lO-’rnol.

The entropy difference of an ideal gas at 20°C and at -196°C is

AS’ = nCpln(T,/T2) = 0.33 cal/K ,

and the entropy change at phase transition is

AS” = nL/Tz = 0.64 cal/K.

Therefore AS = AS’ + AS’’ = 0.97 cal/K.

1048
A Carnot engine is made to operate as a refrigerator. Explain in detail,
with the aid of (a) a pressure-volume diagram, (b) an enthalpy-entropy
diagram, all the processes which occur during a complete cycle or operation.
This refrigerator freezes water at 0°C and heat from the working sub-
stance is discharged into a tank containing water maintained at 20°C. De-
termine the minimum amount of work required to freeze 3 kg of water.
(SVNY, Buflalo)

V S

[a) (b)

Fig. 1.16.

Solution:

(a) As shown in Fig. l.l6(a),

1-2: adiabatic compression,

2-3: isothermal compression,

3-4: adiabatic expansion,

4-1: isothermal expansion.

(b) As shown in Fig. l.l6(b):