A paramagnetic salt of mass m is held at temperature T in a magnetic field H. If S
is the entropy of the salt and M is its magnetization, then dG = -SdT - MdH,
where G is the Gibbs free energy. If the magnetic field is changed adiabatically by
ΔH → 0 and the corresponding infinitesimal changes in entropy and temperature
are ΔS and ΔT, then which of the following statements are correct
Options:
(A) ΔS = - 1
T ൬𝜕G
𝜕T൰
ு
ΔT
(B) ΔS = 0
(C) ΔT = -
ቀ𝜕M
𝜕T ቁ
ு
ቀ𝜕S
𝜕Tቁ
ு
ΔH
(D) ΔT = 0
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.47)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Electromagnetic Theory:
- 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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