$A$ cylinder of fixed capacity $67.2 \text{ litres}$ contains helium gas at $STP$. The amount of heat needed to raise the temperature of the gas in the cylinder by $20^{\circ} C$ is: (in $\text{ J}$)

Explain the difference between the expressions $C_P - C_V = R$,$C_P - C_V = \frac{R}{J}$,and $C_P - C_V = \frac{r}{J}$.

What is the relationship between the internal energy $U$ of an ideal gas and its pressure $P$ and volume $V$?

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 ......... $J/cal$.

The amount of heat energy required to raise the temperature of $1\,g$ of helium from $T_1\,K$ to $T_2\,K$ is

One mole of an ideal monoatomic gas is heated at a constant pressure from $0^{\circ} C$ to $100^{\circ} C$. The change in the internal energy of the gas is (Given,$R = 8.32 \text{ J mol}^{-1} \text{ K}^{-1}$):