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? $(R = 2 \, cal/mol \cdot K)$

What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

$Assertion :$ 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.

For a monoatomic ideal gas,the universal gas constant $R$ is $n$ times the molar heat capacity at constant pressure $C_P$. Here,$n$ is ......

$40 \, \text{calories}$ of heat is needed to raise the temperature of $1 \, \text{mole}$ of an ideal monoatomic gas from $20^{\circ}C$ to $30^{\circ}C$ at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $(R = 2 \, \text{cal} \, \text{mol}^{-1} \text{K}^{-1})$ is ..... $\text{calories}$.

Explain the specific heat capacity of water based on the kinetic theory of matter.