The ratio of the specific heats $\frac{C_{p}}{C_{v}}=\gamma$ in terms of degrees of freedom $n$ is given by

$A$ cylinder of fixed capacity of $44.8 \, L$ contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of the gas in the cylinder by $20.0^{\circ} C$ will be .............. $J$ (Given gas constant $R = 8.3 \, J \, K^{-1} \, mol^{-1}$).

The ratio of specific heats $\left(\frac{C_{P}}{C_{V}}\right)$ in terms of degree of freedom $(f)$ is given by

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?

The adiabatic Bulk modulus of a diatomic gas at atmospheric pressure is

Column-$I$ represents the type of gas and Column-$II$ represents the ${C_P}$ value for that type of gas. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Monoatomic gas	$(i)$ ${C_P} = \frac{3}{2}R$
$(b)$ Diatomic gas with vibration	$(ii)$ ${C_P} = \frac{5}{2}R$
	$(iii)$ ${C_P} = \frac{7}{2}R$
	$(iv)$ ${C_P} = \frac{9}{2}R$