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 $20°\text{C}$ is:
[Given that $R=8.31{\text{J mol}}^{-1}{\text{K}}^{-1}$]

• A. $374\text{J}$
• B. $350\text{J}$
• C. $700\text{J}$
• D. $748\text{J}$

Answer 1

The correct option is D $748\text{J}$

Given:
Cylinder capacity $=67.2$ lit
Temperature rise $\Delta T=20°\text{C}$
$R=8.31{\text{J mol}}^{-1}{\text{K}}^{-1}$

As the process is isochoric so, heat required to get the desired temperature rise
$Q=n{c}_v\Delta T$
$=\frac{67.2}{22.4}\times \frac{3R}{2}\times 20=90R$
$=90\times 8.31\simeq 748\text{J}$

Hence option $\left(C\right)$ is correct.