# Low-Temperature Heat Capacity of Hydrogen Molecules

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Hydrogen is the lowest boiling molecular species, remaining a gas down to 20K. At and above room temperature, , the rotational degree of freedom is fully excited; thus the rotational contribution to heat capacity approaches its equipartition value, per mole. Owing to the exceptionally small moment of inertia of , rotation becomes inactive at temperatures below about 50K. However, the heat capacity behaves anomalously as the temperature is lowered. This anomaly was first explained by Dennison in 1927. Since is a homonuclear molecule, only half of its rotational states are accessible. In the singlet nuclear-spin state, known as parahydrogen (*p*-) only even- rotational states are accessible; in the triplet nuclear-spin state, known as orthohydrogen (*o*-) only odd- rotational states are accessible. The molecular partition functions representing the rotational and nuclear spin degrees of freedom are given by

Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: ortho and para rotational heat capacities as functions of temperature

Snapshot 2: 3:1 mixture and equilibrium mixture with catalyst

Snapshot 2: rotational heat capacity of heteronuclear HD molecule

Reference: S. M. Blinder, *Advanced Physical Chemistry; A Survey of Modern Theoretical Principles*, New York: Macmillan, 1969 pp. 475–478.

## Permanent Citation

"Low-Temperature Heat Capacity of Hydrogen Molecules"

http://demonstrations.wolfram.com/LowTemperatureHeatCapacityOfHydrogenMolecules/

Wolfram Demonstrations Project

Published: March 7 2011