A figure plots for dilute carbon monoxide gas (CO

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

Thermal Physics, Ch The classical ideal gas from the partition function

Problem

A figure plots

C_V/Nk_B

for dilute carbon monoxide gas (CO, treated as an ideal gas at every temperature shown, an idealisation at the lowest ones) against

\log_{10}(T/\mathrm{K})

from

1\,\mathrm{K}

4000\,\mathrm{K}

. The plotted curve is described completely by:flat at

1.50

for

T \le 1.5\,\mathrm{K}

;rising steeply between about

2\,\mathrm{K}

and

10\,\mathrm{K}

;flat at

2.50

from about

15\,\mathrm{K}

to about

600\,\mathrm{K}

;rising again above about

800\,\mathrm{K}

, passing through

3.41

3000\,\mathrm{K}

. For CO the characteristic temperatures are

\theta_{\rm rot} = 2.8\,\mathrm{K}

and

\theta_{\rm vib} = 3120\,\mathrm{K}

. Take

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

. Say which internal motion switches on at each of the two steps, quoting the characteristic temperature that places it there, and then: ((a)) read

C_V/Nk_B

off the plot at

1.2\,\mathrm{K}

, at

200\,\mathrm{K}

and at

3000\,\mathrm{K}

; ((b)) convert the

200\,\mathrm{K}

reading into a molar heat capacity

C_V

; ((c)) state the vibrational contribution to

C_V

per molecule at

3000\,\mathrm{K}

, in units of

k_B

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