A closed hollow insulated cylinder is filled with gas at $0^\circ C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on 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
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Using Boyle's law, we have $\frac{V}{T}=$ constant $\Rightarrow \frac{\frac{1}{2}+5}{373} = \frac{\frac{1}{2}-5}{273}$ As the piston moves 5 cm, the length of one side will be $\left(\frac{1}{2}+5\right)$ and other side $\left(\frac{1}{2}-5\right)$. On solving this equation, we get l = 64.6 cm.
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