$A$ polyatomic gas with $6$ degrees of freedom does $25 \ J$ of work when it is expanded at constant pressure. The heat given to the gas is ..... $J$.

Which of the following formulae is wrong?

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

The total internal energy of $2$ mole monoatomic ideal gas at temperature $T=300\,K$ will be ...........$J$. (Given $R = 8.31\,J/mol\cdot K$)

$70 \, cal$ of heat are required to raise the temperature of $2 \, moles$ of an ideal gas at constant pressure from $30^{\circ}C$ to $35^{\circ}C$. The amount of heat required to raise the temperature of the same gas through the same range ($30^{\circ}C$ to $35^{\circ}C$) at constant volume is ..... $cal$ $(R = 2 \, cal/mol \cdot K)$.

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{P}$ and $C_{V}$ respectively. If $\gamma = \frac{C_{P}}{C_{V}}$ and $R$ is the universal gas constant,then $C_{V}$ is equal to