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(B) Let the total length of the cylindrical vessel be $L$. Initially,the piston is at the midpoint,so the initial length of the gas column is $V_1 \pr

Vedclass · Accepted Answer

$27.3$

Vedclass · Answer

(B) Let the total length of the cylindrical vessel be $L$. Initially,the piston is at the midpoint,so the initial length of the gas column is $V_1 \propto L/2$ at $T_1 = 0^{\circ} C = 273 ~K$.When heated to $T_2 = 100^{\circ} C = 373 ~K$,the piston moves by $5 ~cm$,so the new length of the gas column is $V_2 \propto (L/2 + 5)$.Since the pressure remains constant (as the piston is weightless and moves freely),we apply Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.Substituting the values: $\frac{L/2}{273} = \frac{L/2 + 5}{373}$.Cross-multiplying: $373(L/2) = 273(L/2 + 5)$.$373(L/2) = 273(L/2) + 1365$.$100(L/2) = 1365$.$L/2 = 13.65 ~cm$.Therefore,$L = 27.3 ~cm$.

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