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(D) Let the total length of the cylinder be $L = 2l$, where $l$ is the initial length of each side.Initially, the temperature on both sides is $T_1 =

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$64.6$

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(D) Let the total length of the cylinder be $L = 2l$, where $l$ is the initial length of each side.Initially, the temperature on both sides is $T_1 = 0^{\circ} C = 273 \,K$.After heating one side to $T_2 = 100^{\circ} C = 373 \,K$, the piston shifts by $x = 5 \,cm$.The new lengths are $l_1 = l + 5$ and $l_2 = l - 5$.Since the pressure remains constant (piston is free to move), by Charles's Law, $\frac{V_1}{V_2} = \frac{T_1}{T_2}$.Since the cross-sectional area is constant, $\frac{l+5}{l-5} = \frac{373}{273}$.Applying componendo and dividendo: $\frac{(l+5) + (l-5)}{(l+5) - (l-5)} = \frac{373 + 273}{373 - 273}$.$\frac{2l}{10} = \frac{646}{100}$.$2l = \frac{646 	imes 10}{100} = 64.6 \,cm$.Thus, the total length of the cylinder is $64.6 \,cm$.

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