The rotational partition function of H₂ is : · ABC26PH0199

Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Partition Functions · Exam: CSIR NET DEC 2012 · Marks: 2 · Difficulty: Easy

The rotational partition function of $\mathrm{H_2}$ is :
(a)$\sum_{J=0,1,2\ldots}(2J+1)e^{-\beta hcBJ(J+1)}$
(b)$\sum_{J=1,3,5\ldots}(2J+1)e^{-\beta hcBJ(J+1)}$
(c)$\sum_{J=0,2,4\ldots}(2J+1)e^{-\beta hcBJ(J+1)}$
(d)$\frac{1}{4}\left[\sum_{J=0,2,4\ldots}(2J+1)e^{-\beta hcBJ(J+1)} + 3\sum_{J=1,3,5\ldots}(2J+1)e^{-\beta hcBJ(J+1)}\right]$
Answer
Answer (as printed): D
Explanation
CSIR JUNE 13 12. A system has 100 degenerate energy levels and 100 bosons are kept in it. Find the entropy of the system at equilibrium a) 10-2kb b) 102 kb c) 460.0 kb d) 4.606 kb 9ªª pÆÆ W= (for boson particle) 9ªª! 9ªª pÆÆ S= = 𝐾S 𝑙𝑛𝑊 =𝐾S 𝑙𝑛 = 𝐾S 𝑙𝑛1009ªª − 𝑙𝑛100! 9ªª! kB (100ln 100-100ln100+100)=102 kB

Explanation as extracted from the printed page; notation may be imperfect.

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