Chapter 13, Problem 13B.9AE

Interpretation Introduction

Interpretation:

The exact vibrational partition function for ${\text{Br}}_{\text{2}}$ molecule, its comparison with the approximated vibrational function and the temperature at which these two values are within $5\%$ range have to be stated.

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 shown below.

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

The vibrational partition function for molecules is represented as shown  below.

  $q^{\text{V}}=\frac{1}{\text{1}-e^{-\beta hc\tilde{\nu }}}$