$(A)$ The ratio of specific heats is given by $\gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}$, where $f$ is the degree of freedom.For a triatomic rigid g

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$(A)$ The ratio of specific heats is given by $\gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}$, where $f$ is the degree of freedom.For a triatomic rigid gas, $f = 6$, so $\gamma = 1 + \frac{2}{6} = \frac{4}{3}$. $(A-III)$For a diatomic non-rigid gas, $f = 7$, so $\gamma = 1 + \frac{2}{7} = \frac{9}{7}$. $(B-IV)$For a monoatomic gas, $f = 3$, so $\gamma = 1 + \frac{2}{3} = \frac{5}{3}$. $(C-I)$For a diatomic rigid gas, $f = 5$, so $\gamma = 1 + \frac{2}{5} = \frac{7}{5}$. $(D-II)$Thus, the correct match is $A-III, B-IV, C-I, D-II$.

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

Medium

Match the List-$I$ with List-$II$:
List-$I$ List-$II$
$A$. Triatomic rigid gas $I$. $\frac{C_P}{C_V} = \frac{5}{3}$
$B$. Diatomic non-rigid gas $II$. $\frac{C_P}{C_V} = \frac{7}{5}$
$C$. Monoatomic gas $III$. $\frac{C_P}{C_V} = \frac{4}{3}$
$D$. Diatomic rigid gas $IV$. $\frac{C_P}{C_V} = \frac{9}{7}$

Choose the correct answer from the options given below:

JEE MAIN 2025 All JEE MAIN

A
$A-III, B-IV, C-I, D-II$
B
$A-III, B-II, C-IV, D-I$
C
$A-II, B-IV, C-I, D-III$
D
$A-IV, B-II, C-III, D-I$

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Class 11

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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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The graph of specific heat at constant volume $(C_v)$ for a monoatomic gas with respect to temperature $(T)$ is:

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List-$I$	List-$II$
$A$. Triatomic rigid gas	$I$. $\frac{C_P}{C_V} = \frac{5}{3}$
$B$. Diatomic non-rigid gas	$II$. $\frac{C_P}{C_V} = \frac{7}{5}$
$C$. Monoatomic gas	$III$. $\frac{C_P}{C_V} = \frac{4}{3}$
$D$. Diatomic rigid gas	$IV$. $\frac{C_P}{C_V} = \frac{9}{7}$

Similar Questions

For a gas,the difference between the two specific heats is $4150 \ J/kg \ K$. What is the specific heat at constant volume of the gas if the ratio of specific heats is $1.4$ (in $J/kg \ K$)?

For an ideal gas,the molar specific heat at constant pressure is $(7/2) R$. Find the ratio of the molar specific heat at constant pressure to the molar specific heat at constant volume.

One mole of an ideal gas $\left( \frac{C_P}{C_V} = \gamma \right)$ is heated according to the law $P = \alpha V$,where $P$ is the pressure of the gas,$V$ is the volume,and $\alpha$ is a constant. What is the molar heat capacity of the gas in this process?

The graph of specific heat at constant volume $(C_v)$ for a monoatomic gas with respect to temperature $(T)$ is:

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