Hydrogen gas is held at

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Quantum Mechanics · Statistical foundations and the equilibrium ensembles

Deriving the Spectrum, Ch Diatomic rotation-vibration spectra and nuclear spin statistics

Problem

T = 100\,\mathrm{K}

, where

\theta_r = hcB_0/k_{\rm B} = 85.3\,\mathrm{K}

. Levels with

J \ge 5

may be neglected. ((a)) Find the rotational heat capacity per mole, as

C_{\rm rot}/R

, of pure para-hydrogen (even

J

only) and of pure ortho-hydrogen (odd

J

only). ((b)) Find

C_{\rm rot}/R

for normal hydrogen cooled from room temperature without a catalyst, a frozen

3:1

ortho-para mixture. ((c)) Find the para fraction and

C_{\rm rot}/R

of equilibrium hydrogen at

100\,\mathrm{K}

, in which ortho and para interconvert freely. ((d)) Which of the heat capacities in (b) and (c) does a calorimeter measure on a bottle of hydrogen cooled to

100\,\mathrm{K}

over an hour, and why?

Related theory

Quantum Mechanics

Browse the problem library