(A) We know that for an ideal gas,the molar specific heat at constant pressure is $C_p = \left(1 + \frac{f}{2}\right)R$ and at constant volume is $C_v

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(A) We know that for an ideal gas,the molar specific heat at constant pressure is $C_p = \left(1 + \frac{f}{2}\right)R$ and at constant volume is $C_v = \frac{f}{2}R$.The ratio of specific heats is given by $\gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f}$,which implies $\frac{2}{f} = \gamma - 1$,or $\frac{f}{2} = \frac{1}{\gamma - 1}$.Substituting this into the expression for $C_p$:$C_p = \left(1 + \frac{1}{\gamma - 1}\right)R$$C_p = \left(\frac{\gamma - 1 + 1}{\gamma - 1}\right)R$$C_p = \frac{\gamma R}{\gamma - 1}$.

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

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If $C_p$ and $C_v$ are molar specific heats of an ideal gas at constant pressure and volume respectively,if $\gamma$ is the ratio of the two specific heats and $R$ is the universal gas constant,then $C_p$ is equal to

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A
$\frac{R \gamma}{\gamma-1}$
B
$\gamma R$
C
$\frac{1+\gamma}{1-\gamma}$
D
$\frac{R}{\gamma-1}$

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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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On giving an equal amount of heat at constant volume to $1 \, mol$ of a monoatomic and a diatomic gas,the rise in temperature $(\Delta T)$ is more for:

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For a diatomic gas,write the value of the ratio of $C_P$ and $C_V$.

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For a rigid diatomic molecule,the universal gas constant $R = n C_P$,where $C_P$ is the molar specific heat at constant pressure and $n$ is a number. Hence,$n$ is equal to

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The amount of heat energy required to raise the temperature of $1\, g$ of Helium at $NTP$ from $T_1\, K$ to $T_2\, K$ is:

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

If $C_p$ and $C_v$ are molar specific heats of an ideal gas at constant pressure and volume respectively,if $\gamma$ is the ratio of the two specific heats and $R$ is the universal gas constant,then $C_p$ is equal to

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On giving an equal amount of heat at constant volume to $1 \, mol$ of a monoatomic and a diatomic gas,the rise in temperature $(\Delta T)$ is more for:

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