Problems and Solutions on Thermodynamics and Statistical Mechanics

55

Solution:
(a) The change in entropy of the system is

Tf Mc,dX Tf

Ti

• Mc, In -.

The change in entropy of the heat source is

The total change in entropy is

AS = AS, +AS, = Mc,

N-1

AS= lim C AS, ,

AN+w AT-0 n=O

where

• Tj + nAT + (n + 1)AT

is the change in entropy of the (n + 1)th contact. Thus

(c) The function f(z) = z - Ins - 1 > 0 if z > 0 and z # 1. Thus

in (a) AS = Mc,f(Ti/Tf) > 0, that is, the entropy is increased. We know

the process is irreversible from the second law of thermodynamics. In (b)

AS = 0, the process is reversible.

1060

A material is brought from temperature 3 to temperature Tf by plac-

ing it in contact with a series of N reservoirs at temperatures Ti + AT, Ti +