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(B) Let the total length of the cylinder be $L$. Initially, the piston is at the midpoint, so the length of the gas column is $L_1 = L/2$. The initial

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$27.3$

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(B) Let the total length of the cylinder be $L$. Initially, the piston is at the midpoint, so the length of the gas column is $L_1 = L/2$. The initial temperature is $T_1 = 0^{\circ} C = 273 \, K$.When the gas is heated to $T_2 = 100^{\circ} C = 373 \, K$, the piston moves by $5 \, cm$. The new length of the gas column is $L_2 = (L/2) + 5$.Assuming the pressure remains constant (as the piston is weightless and moves freely), we use Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.Since the cross-sectional area $A$ is constant, $V = A 	imes 	ext{length}$, so $\frac{L_1}{T_1} = \frac{L_2}{T_2}$.Substituting the values: $\frac{L/2}{273} = \frac{(L/2) + 5}{373}$.$373(L/2) = 273(L/2 + 5)$.$373(L/2) = 273(L/2) + 273 	imes 5$.$(373 - 273)(L/2) = 273 	imes 5$.$100(L/2) = 1365$.$L/2 = 13.65$.$L = 27.3 \, cm$.

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