In the case of a diatomic gas,the fraction of heat supplied at constant pressure that is used for the expansion of the gas is:

If $c_p$ and $c_v$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M$,then which of the following relations holds true,where $R$ is the molar gas constant?

Given below are observations on molar specific heats at room temperature of some common gases.

Gas	Molar specific heat $(C_v)$ $(cal\, mol^{-1}\, K^{-1})$
Hydrogen	$4.87$
Nitrogen	$4.97$
Oxygen	$5.02$
Nitric oxide	$4.99$
Carbon monoxide	$5.01$
Chlorine	$6.17$

The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically,molar specific heat of a monatomic gas is $2.92 \; cal/mol\; K$. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?

$Assertion:$ At a given temperature,the specific heat of a gas at constant pressure $(C_p)$ is always greater than its specific heat at constant volume $(C_v)$.
$Reason:$ When a gas is heated at constant volume,some extra heat is needed compared to that at constant pressure for doing work in expansion.

The molar specific heats of an ideal gas at constant pressure and constant 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:

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.