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

Given, Volume $=\text{44}.\text{8lit}=\text{44}.\text{8}\times \text{1}{0}^{\text{−3}}{\text{m}}^3$

We know that, One mole of any ideal gas at STP occupies a volume of 22.4 litre therefore, cylinder of fixed capacity 44.8 litre must contain 2 moles of helium at STP. As helium is monatomic gas. For helium, ${\text{C}}_{\text{v}}=\text{3/2R}$

Now, Heat needed to raise the temperature $\text{Q}=\text{nCvdT}=\text{2}\times (\text{3}/\text{2})\text{R2}0 =\text{3}\times \text{8}.\text{3}\times \text{2}0=\text{498 J}$