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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 each side is $l = L/2$.According to Charles'

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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 each side is $l = L/2$.According to Charles's law, at constant pressure, $V \propto T$, which implies $l \propto T$ for a cylinder of uniform cross-section.Let the initial temperature be $T_1 = 0^{\circ} C = 273 ~K$ and the final temperature of the heated side be $T_2 = 100^{\circ} C = 373 ~K$.When the piston moves by $5 ~cm$, the length of the heated side becomes $(l + 5)$ and the length of the other side becomes $(l - 5)$.Applying the ratio: $\frac{l+5}{l-5} = \frac{373}{273}$.Using componendo and dividendo: $\frac{(l+5) + (l-5)}{(l+5) - (l-5)} = \frac{373 + 273}{373 - 273}$.$\frac{2l}{10} = \frac{646}{100}$.$2l = 64.6 ~cm$.Since the total length of the cylinder is $L = 2l$, the total length is $64.6 ~cm$.

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