Q 11-12-013JEE MainEAMCET 2011 (Engineering)Hard
A closed hollow insulated cylinder is filled with gas at $0°$C and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to $100°$C. If the piston moves $5$ cm, the length of the hollow cylinder is
Answer: (D) $64.6$ cm
Let each half have length $x$ initially, at pressure $P$. After heating, both sides have the same pressure $P'$.
Heated side: $\dfrac{P'(x + 5)}{373} = \dfrac{Px}{273}$. Other side (still at $273$ K): $P'(x - 5) = Px$.
Dividing: $\dfrac{x + 5}{x - 5} = \dfrac{373}{273} \Rightarrow 100x = 3230 \Rightarrow x = 32.3$ cm.
Length of cylinder $= 2x = 64.6$ cm.
Solution by Sreeraj P, M.Sc Physics