# A cylinder with fixed capacity of 67.2 lit contains helium gas at STP.

Question:

A cylinder with fixed capacity of $67.2$ lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20^{\circ} \mathrm{C}$ is : [Given that $\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ ]

1. (1) $350 \mathrm{~J}$

2. (2) $374 \mathrm{~J}$

3. (3) $748 \mathrm{~J}$

4. (4) $700 \mathrm{~J}$

Correct Option: , 3

Solution:

(3) As the process is isochoric so,

$\mathrm{Q}=\mathrm{nc}_{\mathrm{v}} \Delta \mathrm{T}=\frac{67.2}{22.4} \times \frac{3 \mathrm{R}}{2} \times 20=90 \mathrm{R}=90 \times 8.31 \simeq 748 \mathrm{j}$