Measurement on a dilute gas near gives a molar heat capacity at constant pressure of

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · Statistical mechanics of ideal classical systems

Thermal Physics, Ch The first law: work, heat and internal energy

Problem

Measurement on a dilute gas near

300\,\mathrm{K}

gives a molar heat capacity at constant pressure of

29.2\,\mathrm{J\,K^{-1}\,mol^{-1}}

. Treat the gas as ideal with heat capacities constant over the small range of the measurement. Chapter 1 gives

U = \tfrac f2 Nk_BT

for a gas with

f

quadratic energy terms per molecule. Use

R = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}

and

k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}

. ((a)) Find the molar heat capacity at constant volume, and state in one sentence why it is smaller than the constant-pressure value by exactly

R

per mole. ((b)) Using

C_V = (\partial U/\partial T)_V

and the Chapter 1 expression for

U

, find

f

to the nearest integer, and say which molecular motions supply the quadratic terms. ((c)) Find

\gamma

for this gas. ((d)) Find the heat needed per molecule to raise the temperature by

1.00\,\mathrm{K}

at constant volume.

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