Statistics

Step 1: Understanding the total energy.
For a system obeying classical statistics with energy levels

0

E

, the total energy

U

is given by the expected energy of the system, which involves the Boltzmann factor

e%5E%7BE%2FkT%7D

. The formula for the total energy is

U%20%3D%20%5Cfrac%7BNE%7D%7B1%20%2B%20e%5E%7BE%2FkT%7D%7D

.
Step 2: Heat capacity.
The heat capacity is given by

C%20%3D%20%5Cfrac%7BdU%7D%7BdT%7D

. Differentiating the expression for

U

with respect to

T

gives the heat capacity as

C%20%3D%20k%20%5Cfrac%7BNE%7D%7BkT%7D

.
Step 3: Conclusion.
Thus, the correct answer is option (A) because both the expressions for

U

and

C

match those derived.

Chapter Questions
1 MCQs