Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodyomics 11

1012
One mole of a monatomic perfect gas initially at temperature To ex-
pands from volume Vo to 2VOl (a) at constant temperature, (b) at constant
pressure.
Calculate the work of expansion and the heat absorbed by the gas in
each case.
(Wisconsin)

Solution:
(a) At constant temperature To, the work is

2vo

W=LB pdV = RTo lo dV/V = RTo In2.

As the change of the internal energy is zero, the heat absorbed by the gas

is

Q = W = RTo ln2.

(b) At constant pressure p, the work is

The increase of the internal energy is

3 3 3

2 2 2

AU = C,AT = -RAT = -pAV = -pVd

3

-RTo.

2

Thus the heat absorbed by the gas is

5

2

Q=AU+W=-RTo.

101s

For a diatomic ideal gas near room temperature, what fraction. of the

heat supplied is available for external work if the gas is expanded at constant

pressure? At constant temperature?

(Wisconsin)