Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 57

1061
The specific heat of water is taken as 1 cal/g.K, independent of tem-
perature, where 1 calorie = 4.18 joules.
(a) Define the specific heat of a substance at constant pressure in terms
of such quantities as Q (heat), S (entropy), and T (temperature).

(b) One kg of water at 0°C is brought into sudden contact with a large
heat reservoir at 100°C. When the water has reached 1OO"C, what has been
the change in entropy of the water? Of the reservoir? Of the entire system
consisting of both water and the heat reservoir?
(c) If the water had been heated from 0°C to 100°C by first bringing it
into contact with a reservoir at 50°C and then another reservoir at 1OO"C,
what would be the change in entropy of the entire system?
(d) Show how the water might be heated from 0°C to 100°C with

(UC, Berkeley)

negligible change in entropy of the entire system.

Solution:

(a)cp=(g),=~(g). P

(b) The change in the entropy of the water is

and the change in entropy of the reservoir is

AS, = -cP- T2 - Ti = -0.268

T2

cal/g,K.

Thus AS = 0.044 cal/g.K.

(c) In this process, the change in entropy of the water is still AS': =

0.312 cal/g,K, while that of the reservoir is

AS; = -^1 x (50 - 1) -^1 X (100 - 50)

273 + 50 273 + 100

= -0.289 cal/g.K I

So that AS' = AS: + AS; = 0.023 cal/g.K.

(d) Divide the range of temperature 0°C - 100°C into N equal parts,

with N >> 1.