The molar specific heats of an ideal gas at c | vedclass

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(A) According to Mayer's relation for an ideal gas,the difference between molar specific heat at constant pressure $(C_{P})$ and molar specific heat a

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$\frac{R}{\gamma - 1}$

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(A) According to Mayer's relation for an ideal gas,the difference between molar specific heat at constant pressure $(C_{P})$ and molar specific heat at constant volume $(C_{V})$ is equal to the universal gas constant $(R)$:$C_{P} - C_{V} = R$Given the adiabatic index $\gamma$ is defined as the ratio of molar specific heats:$\gamma = \frac{C_{P}}{C_{V}}$From this,we can express $C_{P}$ as:$C_{P} = \gamma C_{V}$Substitute this expression for $C_{P}$ into Mayer's relation:$\gamma C_{V} - C_{V} = R$Factor out $C_{V}$:$C_{V}(\gamma - 1) = R$Solving for $C_{V}$:$C_{V} = \frac{R}{\gamma - 1}$

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

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{P}$ and $C_{V}$ respectively. If $\gamma = \frac{C_{P}}{C_{V}}$ and $R$ is the universal gas constant,then $C_{V}$ is equal to

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