The molar specific heat of an ideal gas at constant pressure and constant volume is $C_{p}$ and $C_{v}$ respectively. If $R$ is the universal gas constant and $\gamma = \frac{C_p}{C_v}$,then $C_v =$

The energy required to raise the temperature of $5 \, \text{moles}$ of $H_2$ gas from $30^{\circ}C$ to $60^{\circ}C$ at constant pressure is ......... $\text{calories}$ $(R = 2 \, \text{cal/mol} \cdot \text{K})$.

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

One mole of an ideal gas requires $207 \, J$ of heat to raise the temperature by $10 \, K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 \, K$,the heat required is ...... $J$ (Given the gas constant $R = 8.3 \, J/mol \cdot K$)

The graph of specific heat at constant volume $(C_v)$ for a monoatomic gas with respect to temperature $(T)$ is:

The specific heat at constant volume for the monoatomic argon is $0.075 \, kcal/kg-K$,whereas its gram molecular specific heat $C_V = 2.98 \, cal/mole/K$. The mass of the argon atom is (Avogadro's number $= 6.02 \times 10^{23} \, molecules/mole$)