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  4. A closed hollow insulated cylinder is filled with gas at 0° 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° C. If the piston moves 5 cm the length of the hollow cylinder is

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Q. 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 $5\, cm$ the length of the hollow cylinder is

Kinetic Theory

Solution:

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
$\left(\frac{l}{2}+5\right)$ and other side $\left(\frac{l}{2}-5\right).$
On solving this equation, we get $l=64.6\, cm$.