The molar specific heat at constant pressure for a monoatomic gas is

On giving an equal amount of heat at constant volume to $1 \, mol$ of a monoatomic and a diatomic gas,the rise in temperature $(\Delta T)$ is more for:

If $\Delta Q$ is the amount of heat supplied to $n$ moles of a diatomic gas at constant pressure,$\Delta U$ is the change in internal energy,and $\Delta W$ is the work done,then the ratio $\Delta W : \Delta U : \Delta Q$ is

The value of the gas constant $(R)$ calculated from the perfect gas equation is $8.32 \ J/mol \cdot K$,whereas its value calculated from the knowledge of $C_P$ and $C_V$ of the gas is $1.98 \ cal/mol \cdot K$. From this data,the value of $J$ is ......... $J/cal$.

$5 \ \text{moles}$ of an unknown gas is heated at constant volume from $10^\circ \text{C}$ to $20^\circ \text{C}$. The molar specific heat of this gas at constant pressure is $c_p = 8 \ \text{cal/mol} \cdot ^\circ \text{C}$ and the gas constant is $R = 8.36 \ \text{J/mol} \cdot ^\circ \text{C}$. The change in the internal energy of the gas is . . . . . . calorie.

If the molar specific heat at constant volume is $\frac{3R}{2}$,then the adiabatic index $\gamma$ is: