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 $100^{\circ}$ C .If the piston moves 5cm the length of the hollow cylinder is

13.65 cm

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27.3 cm

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38.6 cm

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64.6 cm

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Solution

The correct option is D 64.6 cm
Using Boyle's law, we have $\frac{V}{T} =$ constant

$\Rightarrow \frac{\frac{l}{2} + 5}{373} = \frac{\frac{l}{2} - 5}{273}$
As the piston moves 5 cm, the length of one side will be $(\frac{l}{2} + 5)$ and other side $(\frac{l}{2} - 5)$ . On solving this equation, we get $I = 64.6 c m .$

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