Problems and Solutions on Thermodynamics and Statistical Mechanics

156 Problems €4 Sdutiom on Thermodynam'ca €4 Statistical Mechanics

(c) When equilibrium is reached, aT/dt = 0; hence V2T = 0.
The boundary conditions are T(r1) = TI and T(r2) = T2.
Choosing the cylindrical coordinate system and solving the Laplace
equation, we obtain the temperature between rl and 7-2:

1

T(r) = - rl

In -

r2

r

r2

TI In - - T2 In -

we obtain the rate at which the heat is lost:

7-2

rl

q = 2wLH = 27rk(T1 - T2)L/ln -.

1158

A uniform non-metallic annular cylinder of inner radius rl , outer radius

r2, length lo is maintained with its inner surface at 100°C and its outer

surface at 0°C.

(a) What is the temperature distribution inside?

(b) If it is then placed in a thermally insulated chamber of negligible

heat capacity and allowed to come to temperature equilibrium, will its

entropy increase , decrease or remain the same? Justify your answer.

( Wisconsin)

Fig. 1.47.