Chapter 13, Problem 13C.8P

(a)

Interpretation Introduction

Interpretation:

The expression for temperature is $\beta =\frac{1}{\epsilon }\ln \left(1+\frac{1}{a}\right)$ and the temperature of the system has to be derived.

Concept introduction:

Statistical thermodynamics is used to describe all the possible configurations in a system at given physical quantities such as pressure, temperature, and a number of particles in the system.  The important quantity in the thermodynamic is partition function that is represented as,

  $q\equiv {\displaystyle \sum _i{g}_i{e}^{-\beta {\in }_i}}$

The mean vibrational energy is given by the equation

  $\langle {\epsilon }^v\rangle =\frac{hc\tilde{v}}{{\text{e}}^{\beta hc\tilde{v}}-1}$

(b)

Interpretation Introduction

Interpretation:

The molecular partition function when mean energy is $a\epsilon$ has to be stated.

Concept introduction:

The same concept introduction as discussed in part (a).