4AB › Chemistry PYQ › CSIR-NET › June 2017 › Q71Q71 · CSIR-NET Chemistry, June 2017 Paper: CSIR-NET June 2017 · Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Statistical Thermodynamics – General · Marks: 2 · Difficulty: Medium
Consider a system of three particles which can occupy energy levels with energy $0, \in$ and $2 \in$, such that the total energy $\mathrm{E}=4 \in$. Cases $\mathrm{A}, \mathrm{B}$ and C correspond to spin $\frac{1}{2}$ fermions, spin 0 bosons, and classically distinguishable particles, respectively. The correct ordering of entropy is
(a) $\mathrm{S}_{\mathrm{A}}>\mathrm{S}_{\mathrm{B}}>\mathrm{S}_{\mathrm{C}}$
(b) $\mathrm{S}_{\mathrm{B}}>\mathrm{S}_{\mathrm{A}}>\mathrm{S}_{\mathrm{C}}$
(c) $\mathrm{S}_{\mathrm{C}}>\mathrm{S}_{\mathrm{B}}>\mathrm{S}_{\mathrm{A}}$
(d) $\mathrm{S}_{\mathrm{C}}>\mathrm{S}_{\mathrm{A}}>\mathrm{S}_{\mathrm{B}}$
Answer Answer: D ✓ checked by 4AB · confidence high
Explanation For E = 4ε: distinguishable particles have 6 arrangements; spin-½ fermions have 4 (each doubly occupied level needs opposite spins, singly occupied levels carry a spin choice); spinless bosons have only 2. S_C > S_A > S_B.
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