Chapter 17, Problem 17.42E

Interpretation Introduction

Interpretation:

The $E$ for a particle in a one-dimensional and two-dimensional box is to be determined.

Concept introduction:

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

$q\equiv {\displaystyle \sum _i{g}_i{e}^{-{\in }_i/\text{kT}}}$

Where,

• $g_i$ represents the degeneracy.

• ${\in }_i$ represents the energy of $i^{th}$ microstate.

• $k$ represents the Boltzmann constant with value $1.38\times {10}^{-23}\text{J}/\text{K}$.

• $T$ represents the temperature $\left(\text{K}\right)$.

It is also called as canonical ensemble partition function.