Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 79

(a) Q = T[S(T,2Lo) - SO] = -aTLo (1 + $Tao).

= T- a2s
aLaT
L; L
= -aT { + - + T (2g + g) a01 }, Z 0
[-- L2 Lo
Thus CL = CL (T, L).

1082
Information: If a rubber band is stretched adiabatically, its tempera-
ture increases.

(a) If the rubber band is stretched isothermally, does its entropy in-

(b) If the rubber band is stretched adiabatically, does the internal

crease, decrease, or stay the same?

energy increase, decrease, or stay the same?

Solution:

done on it is

( wis co nsin)

(a) We assume that when the rubber band is stretched by dx the work

dW = kxdx ,

where k, the elastic coefficient, is greater than 0. From the formula dF =

-SdT + kxdx, we can obtain the Maxwell relation:

(g)T = - (kg)z = 0

Hence the entropy of the rubber band stays the same while it is stretched

isothermally.

(EjS =

(b) According to the formula dU = TdS + kxdx, we have

kx > 0, that is, its internal energy increases while it is stretched adiabati-

cally.