For a certain gas the heat capacity at constant pressure is greater than that at constant volume by $29.1 J / K$ . If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at constant volume and at constant pressure.

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Solution

Fro,m the given information,

$C_{P} - C_{V} = 29.1 J / K$

Also, since the gas is diatomic and do not vibrate, degrees of freedom is $5$ .

Hence,

$\frac{C_{P}}{C_{V}} = γ = \frac{f + 2}{f} = \frac{7}{5}$

Thus,

$\frac{2}{5} C_{V} = 29.1 J / K$

$C_{V} = 72.75 J / K$

Also, $C_{P} = \frac{7}{5} C_{V} = 101.85 J / K$

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\begin{matrix} Column I & Column II i. If the gas is monoatomic, heat capacity at constant volume & a. 131 J/K ii. If the gas is monoatomic, heat capacity at constant pressure & b. 43.7 J/K iii. If the gas is rigid diatomic, heat capacity at constant pressure & c. 72.7 J/K iv. If the gas is vibrating diatomic, heat capacity at constant pressure & d. 102 J/K \end{matrix}

List 1	List 2
If the gas is monatomic, heat capacity at constant volume	131 J/K
If the gas monatomic, heat capacity at constant pressure	43.7 J/K
If the gas is rigid diatomic, heat capacity at constant pressure	72.7 J/K
If the gas is vibrating diatomic, heat capacity at constant pressure	102 J/K

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\begin{matrix} Column I & Column II i. If the gas is monoatomic, heat capacity at constant volume & a. 131 J/K ii. If the gas is monoatomic, heat capacity at constant pressure & b. 43.7 J/K iii. If the gas is rigid diatomic, heat capacity at constant pressure & c. 72.7 J/K iv. If the gas is vibrating diatomic, heat capacity at constant pressure & d. 102 J/K \end{matrix}

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