Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 109

Therefore, the final temperature of the water is 0°C.

(b) The heat absorbed by the ice block is

92 = /[I - rl(t)]dQ = mCv L:I3 YdT = 8.5 x lo4 cal.

This heat can melt ice to the amount of

Q2 - 8.5 x lo4

MI- -

&ion 80

= 1.06 kg.

(c) The work done by the engine is

W = Q1 - Q2 = 1000 x 100 x 1 - 8.5 x lo4 = 1.5 x lo4 cal.

1111

What is the smallest possible time necessary to freeze 2 kg of water at

0°C if a 50 watt motor is available and the outside air (hot reservoir) is at

27OC?

( Wisconsin)

Solution:

When 2 kg of water at 0°C becomes ice, the heat released is

92 = 1.44 x 2 x 103/18 = 1.6 x lo2 kcal.

The highest efficiency of the motor is

Thus,

If we use the motor of P = 50 W, the smallest necessary time is