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
Concept. Gas law on each side of the piston; at equilibrium both sides have the same pressure.
Step 1. Equations. Each half has length $x$ at pressure $P$:
- heated side: $\dfrac{P'(x + 5)}{373} = \dfrac{Px}{273}$;
- other side (still $273$ K): $P'(x - 5) = Px$.
Step 2. Divide.
$$\frac{x + 5}{x - 5} = \frac{373}{273} \;\Rightarrow\; 100x = 3230 \;\Rightarrow\; x = 32.3\ \text{cm}$$
Step 3. Length. $2x = 64.6$ cm.
Answer. $64.6$ cm (Option D).
Solution by Sreeraj P, M.Sc Physics