Thermal Physics - Thermal Equilibrium

Suppose that a system in a quantum state i has energy E_i. In thermal equilibrium, the expression

represents which of the following?

A. The average energy of the system
B. The partition function
C. Unity
D. The probability to find system with energy E_i
E. The entropy of the system

 (GR0177 #98)

Solution:

The units of the given expression are the units of E_i which as given is energy.

The average energy is given by

<E> = ^{∑_i E_i e−E_i/kT} / _Z

where

Z = ∑_i e^−E_i/kT

is the partition function.

Answer: A