Subtopic: Partition Function & Thermodynamic Connection
Question Statement:
As shown in the figure, inverse magnetic susceptibility (1/x) is plotted as a
function of temperature (T) for three different materials in paramagnetic
states.
%.
T
(Curie temperature of ferromagnetic material =Tc
Néel temperature of antiferromagnetic material= TN)
Choose the correct statement from the following
(A) Material 1 is antiferromagnetic (T < TN), 2 is paramagnetic, and 3 is
ferromagnetic (T < Tc).
(B) Material 1 is paramagnetic, 2 is antiferromagnetic (T < TN), and 3 is
(C) Material 1 ferromagnetic (T < Tc), 2 is antiferromagnetic (T < TN), and 3 is
paramagnetic.
(D) Material 1 is ferromagnetic (T < Tc), 2 is paramagnetic, and 3 is
antiferromagnetic (T < TN).
Options:
(A) Material 1 is antiferromagnetic (T < TN), 2 is paramagnetic, and 3 is ferromagnetic (T < Tc).
(B) Material 1 is paramagnetic, 2 is antiferromagnetic (T < TN), and 3 is
(C) Material 1 ferromagnetic (T < Tc), 2 is antiferromagnetic (T < TN), and 3 is paramagnetic.
(D) Material 1 is ferromagnetic (T < Tc), 2 is paramagnetic, and 3 is antiferromagnetic (T < TN).
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.51 / PH Q.41)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Statistical Ensembles & Partition Functions* (`Partition Function & Thermodynamic Connection`) | **Section**: *Section 5: Thermodynamics and Statistical Physics*
- **Question Type**: **MCQ** | **Marks**: **2 Marks** | **Negative Marks**: **0.67**
- **Governing Principles**: Solved directly by applying fundamental laws of **Statistical Ensembles & Partition Functions**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **A**.
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