The formula for energy E of a photon gas at temperature T in a two-dimensional box at
equilibrium with g2d(𝜈) denoting the density of states of photons is given below where
symbols 𝜈, ℎ and kB have their standard meaning. The specific heat (CV) of this photon
gas obeys
E = ∫ d𝜈 g2d(𝜈)
∞
0
ℎ𝜈
exp ( ℎ𝜈
kBT) - 1
Options:
(A) CV ∝ T
(B) CV ∝ T2
(C) CV ∝ T3
(D) CV ∝ T4
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.18)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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