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

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 $R = 8.3 \, J/mol \cdot K$)

$70 \, cal$ 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 ..... $cal$ $(R = 2 \, cal/mol \cdot K)$.

According to the law of equipartition of energy, the molar specific heat of a diatomic gas at constant volume, where the molecule has one additional vibrational mode, is:

The heat energy that must be supplied to $14 \ g$ of nitrogen at room temperature to raise its temperature by $48^{\circ} C$ at constant pressure is (Molecular weight of nitrogen $= 28, R =$ gas constant,$C_p = \frac{7}{2} R$ for diatomic gas). (in $R$)

The ratio of the molar specific heat capacities of monatomic and diatomic gases at constant pressure is (in $: 7$)