The specific heat Cp(T) of one mole of a material as a function of temperature T is given
as Cp(T) = AT + BT3, where A = 0.695 mJ. mol-1. K-2 and B = 0.045 mJ. mol-1. K-4.
When T is changed from 1 K to 10 K at constant pressure, then the change in entropy
ΔS in mJ. mol-1. K-1 (rounded off to one decimal place) is _____
Official Answer Key:
21.1 to 21.3
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.33)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 5: Thermodynamics and Statistical Physics* | **Topic**: *Classical Thermodynamics* (`Entropy & Thermodynamic Potentials (U, H, F, G)`)
- **Question Type**: **NAT** | **Marks**: **1 Mark**
- **Theoretical Framework**: Governed by foundational physical principles in **Classical Thermodynamics** (`Entropy & Thermodynamic Potentials (U, H, F, G)`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **2.5**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Numerical value: 2.5**.
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