A closed hollow insulated cylinder is filled with gas at $0^{\circ} \mathrm{C}$ and also contains an…
A closed hollow insulated cylinder is filled with gas at $0^{\circ} \mathrm{C}$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} \mathrm{C}$. If the piston moves $5 \mathrm{~cm}$. The length of the hollow cylinder is
$15.65 \mathrm{~cm}$
$27.3 \mathrm{~cm}$
$38.6 \mathrm{~cm}$
$64.6 \mathrm{~cm}$
Solution
From Charle's law, $\frac{V_1}{V_2}=\frac{T_1}{T_2}$
Volume $(V)$ is proportional to the length of hollow cylinder.
$\begin{aligned} \frac{l_1}{l_2} & =\frac{T_1}{T_2} \\ \frac{l+5}{l-5} & =\frac{273+100}{273+0} \\ \frac{l+5}{l-5} & =\frac{373}{273} \\ \frac{2 l}{10} & =\frac{646}{100} \\ & =\frac{646 \times 10}{2 \times 100}=32.3 \mathrm{~cm}\end{aligned}$
$\begin{aligned} \therefore \text { Length of cylinder } & =2 l=2 \times 32.3 \\ & =64.6 \mathrm{~cm}\end{aligned}$