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(D) Let the total length of the cylinder be $l$. Initially,the piston is at the middle,so the length of the gas column on each side is $l/2$.Since the

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$64.6$

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(D) Let the total length of the cylinder be $l$. Initially,the piston is at the middle,so the length of the gas column on each side is $l/2$.Since the cylinder is insulated and the piston is insulated,the pressure on both sides remains equal at all times.According to Charles's Law,for a constant pressure,$V \propto T$,which implies $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.Let the cross-sectional area be $A$. The volume on the heated side becomes $A(\frac{l}{2} + 5)$ at $T_2 = 373\,K$.The volume on the other side becomes $A(\frac{l}{2} - 5)$ at $T_1 = 273\,K$.Equating the ratios: $\frac{\frac{l}{2} + 5}{373} = \frac{\frac{l}{2} - 5}{273}$.$273(\frac{l}{2} + 5) = 373(\frac{l}{2} - 5)$.$136.5l + 1365 = 186.5l - 1865$.$50l = 3230$.$l = 64.6\,cm$.

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