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Gas in chamber $X$ is heated to expand by 50% of its initial volume. Monatomic gas is there in both chamber. Natural length of spring is $l$ . Initial pressure, volume and temperature on both sides of piston is $P_{0}, V_{0}$ and $T_{0}$ respectively and walls of container and piston are adiabatic.

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Work done by gas in chamber $Y = - \frac{3 P_{0} V_{0}}{2} [2^{\frac{2}{3}} - 1]$

Work done by gas in chamber $Y = - \frac{3 P_{0} V_{0}}{2} [2^{\frac{2}{3}} - 1] + \frac{1}{8} K l^{2}$

Work done by gas in chamber $X = \frac{3 P_{0} V_{0}}{2} [2^{\frac{2}{3}} - 1]$

Work done by gas in chamber $X = \frac{3 P_{0} V_{0}}{2} [2^{\frac{2}{3}} - 1] + \frac{K l^{2}}{8}$

answer is A, D.

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Detailed Solution

Chamber Y.
Compression is adiabatic
$V = \frac{V_{0}}{2}$
$Δ U_{Y} = \frac{3}{2} P_{0} V_{0} (2^{\frac{2}{3}} - 1)$

$W_{Y} = - \frac{3 P_{0} V_{0}}{2} (2^{\frac{2}{3}} - 1)$
Question Image

$P_{x} A = K x + P_{y} A$
$W_{x} = \frac{K l^{2}}{8} + \frac{3 P_{0} V_{0}}{2} (2^{\frac{2}{3}} - 1)$

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