The correct relation between $\gamma = \frac{C_p}{C_v}$ and temperature $T$ is:

Molar specific heat of oxygen at constant pressure $C_p = 7.2 \, cal/mol \cdot ^\circ C$ and $R = 8.3 \, J/mol \cdot K$. At constant volume,$5 \, mol$ of oxygen is heated from $10^\circ C$ to $20^\circ C$. The quantity of heat required is approximately ........ $cal$.

Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and $\gamma_2$ be the similar ratio of a diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $\gamma_1/\gamma_2$ is

The correct relation between the degree of freedom $f$ and the ratio of specific heat $\gamma$ is

To increase the temperature of $2$ moles of an ideal gas by $30^{\circ}C$ to $35^{\circ}C$ at constant pressure,$70 \, cal$ of heat is required. How much heat energy in $cal$ is required to increase the temperature by the same amount at constant volume? $(R = 2 \, cal/mol \cdot K)$

$A$ certain amount of an ideal monatomic gas needs $20 \, J$ of heat energy to raise its temperature by $10^{\circ} C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be ........ $J$.