Q71 · 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.
Study loop for Statistical Thermodynamics