When $300 \ J$ of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$, its temperature rises from $20^{\circ}C$ to $50^{\circ}C$ while keeping its volume constant. The mass of the gas is (approximately) . . . . . . g. (Assume the molar mass of the gas is $28 \ g/mol$ and $R = 8.314 \ J/mol \cdot K$).

$105 \, cal$ of heat is required to raise the temperature of $3 \, moles$ of an ideal gas at constant pressure from $30^{\circ} C$ to $35^{\circ} C$. The amount of heat required in calories to raise the temperature of the gas through the range ($60^{\circ} C$ to $65^{\circ} C$) at constant volume is ........ $cal$ $(\gamma = \frac{C_p}{C_v} = 1.4)$.

$A$ cylinder of fixed capacity of $44.8 \, L$ contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of the gas in the cylinder by $20.0^{\circ} C$ will be .............. $J$ (Given gas constant $R = 8.3 \, J \, K^{-1} \, mol^{-1}$).

The heat energy required to raise the temperature of $5 \, moles$ of an ideal gas by $5 \, K$ at constant pressure is $600 \, J$. How much heat (in $J$) is required to raise the same mass of the same gas by $5 \, K$ at constant volume? (Take $R = 8.3 \, J/mol \cdot K$)

The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2} R$. The gas is made up of molecules which are ( $R$ is the universal gas constant)

The molar heat capacity of an ideal gas at constant volume is $\alpha R$. If $R$ is the universal gas constant,then the ratio $C_P/C_V$ is equal to ...........