(B) Given,$\frac{R}{C_{V}} = 0.4$. From Mayer's relation,$C_{P} - C_{V} = R$,so $C_{P} = C_{V} + R$. Substituting $R = 0.4 C_{V}$,we get $C_{P} = C_{V

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(B) Given,$\frac{R}{C_{V}} = 0.4$. From Mayer's relation,$C_{P} - C_{V} = R$,so $C_{P} = C_{V} + R$. Substituting $R = 0.4 C_{V}$,we get $C_{P} = C_{V} + 0.4 C_{V} = 1.4 C_{V}$. The adiabatic index $\gamma$ is defined as $\gamma = \frac{C_{P}}{C_{V}}$. Therefore,$\gamma = \frac{1.4 C_{V}}{C_{V}} = 1.4$. For a rigid diatomic gas,the degrees of freedom $f = 5$. The adiabatic index is $\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{5} = 1 + 0.4 = 1.4$. Thus,the gas is made up of rigid diatomic molecules.

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

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For a gas,$\frac{R}{C_{V}} = 0.4$,where $R$ is the universal gas constant and $C_{V}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

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polyatomic.
B
rigid diatomic.
C
non-rigid diatomic.
D
monatomic.

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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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For a gas,$\frac{R}{C_{v}} = 0.67$. This gas is made up of molecules which are

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The ratio of the molar specific heat capacities of monatomic and diatomic gases at constant pressure is (in $: 7$)

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$C_v$ and $C_p$ denote the molar specific heat capacities of a gas at constant volume and constant pressure,respectively. Then

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$A$ certain amount of an ideal monatomic gas needs $20 \, J$ of heat energy to raise its temperature by $10^{\circ} C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be ........ $J$.

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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 $IV$. $\frac{C_P}{C_V} = \frac{9}{7}$

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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	$IV$. $\frac{C_P}{C_V} = \frac{9}{7}$

For a gas,$\frac{R}{C_{V}} = 0.4$,where $R$ is the universal gas constant and $C_{V}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

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