Problems and Solutions on Thermodynamics and Statistical Mechanics

76 Problems 6' Solutions on Thermodynamics €4 Statistical Mechanics

where p, V and T are the pressure, volume and temperature, respectively,
A is a constant. The internal energy of the matter is

U = BT" ln(V/Vo) + f(T) ,

where B, n and Vo are all constants, f(T) only depends on the temperature.

Find B and n.

( C USPEA)

Solution:

From the first law of thermodynamics, we have

dU+pdV= 1 dU

[-(-),+$]dV+-(-) 1 au dT.

T T dV T aT

dS =

We substitute in the above the expressions

sure p and get

BTn-' + AT2 dV + ['IF) ~

V

dS =

for internal energy U and pres-

From the condition of complete differential, we have

giving

2AT - BTn-' = 0.

Therefore n = 3, B = 2A.

1080

The following measurements can be made on an elastic band:

(a) The change in temperature when the elastic band is stretched. (In

case you have not tried this, hold the attached band with both hands, test

the temperature by touching the band to your lips, stretch the band and