The amount of heat needed to raise the temperature of $4 \, \text{moles}$ of a rigid diatomic gas from $0^{\circ} \text{C}$ to $50^{\circ} \text{C}$ when no work is done is ......$R$ ($R$ is the universal gas constant).

$Assertion :$ 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.

The difference between the two specific heats of $1\, g$ of helium gas at $NTP$ is .... $cal\, g^{-1} K^{-1}$. (Atomic weight of helium $= 4$ and $J = 4.186 \times 10^7\, erg\, cal^{-1}$)

$A$ mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) is kept at room temperature $\left(27^{\circ} C\right)$. The ratio of the specific heat of these gases at constant volume is:

To increase the temperature of $1$ $mol$ of an ideal gas by $10$ $K$ at constant pressure,$207$ $J$ of heat is required. If the temperature of this gas is increased by $10$ $K$ at constant volume,the heat required is ....... $J$ $(R = 8.3$ $J/mol$ $K)$.

The specific heat at constant pressure and at constant volume for an ideal gas are $C_p$ and $C_v$,and its adiabatic and isothermal elasticities are $E_{\phi}$ and $E_{\theta}$ respectively. The ratio of $E_{\phi}$ to $E_{\theta}$ is