Problems and Solutions on Thermodynamics and Statistical Mechanics

42 Problem d Sdutioru on Thermcdyamics €4 statistical Mechanics

Solution:
The process is irreversible. In order to calculate the change of entropy
of the water and of the whole system, we must construct a reversible process
which has the same initial and final states as the process in this problem.

(a) We assume the process is a reversible process of constant pressure.

The change in entropy of the water is

r373

We substitute m = lkg, and CH,~ = 4.18 J/g into it, and find

ASH,, = 1305 J/K.

(b) The change in entropy of the heat source is

Ash, = -IQI/T = -1000 X 4.18 X 100/373

= -11121 J/K.

Therefore the change of entropy of the whole system is

(c) We can imagine infinitely many heat sources which have infinites-

imal temperature difference between two adjacent sources from O°C to

100°C. The water comes in contact with the infinitely many heat sources

in turn in the order of increasing temperature. This process which allows

the temperature of the water to increase from 0°C to 100°C is reversible;

therefore AS = 0.

1047

Compute the difference in entropy between 1 gram of nitrogen gas at

a temperature of 20°C and under a pressure of 1 atm, and 1 gram of liquid

nitrogen at a temperature -196"C, which is the boiling point of nitrogen,

under the same pressure of 1 atm. The latent heat of vaporization of nitro-

gen is 47.6 cal/gm. Regard nitrogen as an ideal gas with molecular weight

28, and with a temperature-independent molar specific heat at constant

pressure equal to 7.0 cal/mol.K.

(UC, Berkeley)