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

Obtain the value of $\frac{C_{P}}{C_{V}}$ for a polyatomic gas.

What is the correct relationship between molar specific heat at constant pressure $(C_P)$ and constant volume $(C_V)$? ($R$ is the universal gas constant)

At constant volume,the specific heat of a gas is $\frac{3R}{2}$. Then the value of $\gamma$ will be ....

An ideal gas has molar heat capacity $C_V$ at constant volume. The gas undergoes a process where the temperature changes as $T=T_0(1+\alpha V^2)$, where $T$ and $V$ are temperature and volume respectively, and $T_0$ and $\alpha$ are positive constants. The molar heat capacity $C$ of the gas is given as $C=C_V+R f(V)$, where $f(V)$ is a function of volume. The expression for $f(V)$ is

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