Problems and Solutions on Thermodynamics and Statistical Mechanics

Themdpamics 41

1045
A body of constant heat capacity C, and a temperature Ti is put into
contact with a reservoir at temperature Tf. Equilibrium between the body
and the reservoir is established at constant pressure. Determine the total
entropy change and prove that it is positive for either sign of (Tf - Ti)/Tf.
You may regard 1% - Ti\/Tf < 1.

Solution:

Ti = Tf). The change of entropy of the body is

( wis co nsin)

We assume Ti # fi (because the change of entropy must be zero when

The change of entropy of the heat source is

Therefore the total entropy change is

When z > 0 and z # 1, the function f (z) = x - 1 - Ins > 0. Therefore

1046

One kg of H2O at 0°C is brought in contact with a heat reservoir at

(a) what is the change in entropy of the water?

(b) what is the change in entropy of the universe?

(c) how could you heat the water to 100°C so the change in entropy of

100OC. When the water has reached 100°C,

the universe is zero?

( was co nsin)