A cylinder of fixed capacity 67.2 litres contains helium gas at STP. The amount of heat needed to rise the…
A cylinder of fixed capacity 67.2 litres contains helium gas at STP. The amount of heat needed to rise the temperature of the gas in the cylinder by $20^{\circ} \mathrm{C}$ is
$784\ J$
$374\ J$
$1000\ J$
$500\ J$
Solution
Amount of heat needed
$\begin{aligned}
& \mathrm{dQ}=\eta \mathrm{C}_v \mathrm{dT} \eta\left(\frac{3}{2} R\right) d t\left[\because Q=\frac{3}{2} R\right] \\
& =\frac{67.2}{22.4} \times \frac{3}{2} \times R \times d T \\
& =3 \times \frac{831 \times 3}{2} \times 20=784 \mathrm{~J}
\end{aligned}$