Problems and Solutions on Thermodynamics and Statistical Mechanics

308 Problem8 d Solutions on Thermodynamic8 €4 Statistical Mechanics

~1 + A. Hence the partition function of the system is

The free energy is

F = -kTlnZ = -NkTln (e-p'l + e--Bea)

The chemical potential is

The pressure is

The entropy is

-klnN!=Nk

N(&le-@'l + ~2e-P'~)

+ T(e-Pc1 + e-0'2)

The heat capacity at constant pressure is

a

• 
  
  
  
  • NA2 - - NA2
    2kT2 (1 + cosh k) 4kT2 cash (&) *
  
  
  
  

2129
(a) Consider an ideal gas of N particles of mass rn confined to a vol-
ume V at a temperature T. Using the classical approximation for the par-
tition function and assuming the particles are indistinguishable, calculate
the chemical potential p of the gas.

(b) A gas of N particles, also of mass rn, is absorbed on a surface
of area A, forming a two-dimensional ideal gas at temperature T on the