Problems and Solutions on Thermodynamics and Statistical Mechanics

334 Problems €4 Solutions on Thermodynamics d Statistical Mechanics

Keeping the first two terms, we have

N2

2v

= VN (1 + -. (-.I) ,

4ra3

In& = NlnV +In

where r = -.

Hence

3

r

2v

M NlnV - -N2 ,

so that

u==-lnz=-kT, a 3N

aP 2

and

J

C, = -Nk,

2

giving

pv=1+-. rN

NkT 2N

Thus

rN 27ra3

2 3

Ai(T) = - = -N.

2146

Consider a classical system of N point particles of mass m in a volume

V at temperature T. Let U be the total energy of the system, p the pressure.

The particles interact through a two-body central potential