Question

Partition function for a gas of photons is given as \( Z \propto e^{A T^3} \). The specific heat of photon gas varies with temperature as:

• A. \( C_V \propto T \)
• B. \( C_V \propto T^3 \)
• C. \( C_V \propto T^2 \)
• D. \( C_V \propto T^{4/3} \)

Hint:

For a photon gas, the specific heat follows the Stefan-Boltzmann law.

Answer 1

The Correct Option is B

The specific heat is given by:
\[ C_V = \left(\frac{\partial U}{\partial T} \right)_V \] For a photon gas, the internal energy scales as \( U \propto T^4 \), leading to:
\[ C_V \propto T^3 \]