(C) For a monoatomic gas,the degrees of freedom $f = 3$. The ratio of specific heats is $\gamma_1 = 1 + \frac{2}{f} = 1 + \frac{2}{3} = \frac{5}{3}$.F

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(C) For a monoatomic gas,the degrees of freedom $f = 3$. The ratio of specific heats is $\gamma_1 = 1 + \frac{2}{f} = 1 + \frac{2}{3} = \frac{5}{3}$.For a diatomic gas acting as a rigid rotator,the degrees of freedom $f = 5$ ($3$ translational + $2$ rotational). The ratio of specific heats is $\gamma_2 = 1 + \frac{2}{f} = 1 + \frac{2}{5} = \frac{7}{5}$.Therefore,the ratio $\frac{\gamma_1}{\gamma_2} = \frac{5/3}{7/5} = \frac{5}{3} \times \frac{5}{7} = \frac{25}{21}$.

Class 11 Physics Kinetic Theory of Gases Molar Specific Heat of gas and relation between them (Mayer's formula)

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Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of a diatomic gas. Considering the diatomic gas molecule as a rigid rotator,the ratio $\frac{\gamma_1}{\gamma_2}$ is

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A
$\frac{27}{35}$
B
$\frac{35}{27}$
C
$\frac{25}{21}$
D
$\frac{21}{25}$

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Kinetic Theory of Gases

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Molar Specific Heat of gas and relation between them (Mayer's formula)

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Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of a diatomic gas. Considering the diatomic gas molecule as a rigid rotator,the ratio $\frac{\gamma_1}{\gamma_2}$ is

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$176 \text{ grams}$ of $CO_2$ can change its temperature from $0^{\circ} C$ to $30^{\circ} C$ by absorbing $3600 \text{ joules}$ of thermal energy. The molar specific heat of $CO_2$ in $J \ mol^{-1} K^{-1}$ is:

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