A thermally insulated chamber of volume 2V₀ is divided by a frictionless piston of area S into two equal parts A and B. Part A has an ideal gas at pressure P₀ and temperature T₀ and part B is vacuum. A massless spring of force constant K is connected with the piston and the wall of the container as shown. Initially the spring is unstretched. The gas inside chamber A is allowed to expand. Let in equilibrium the spring be compressed by x₀. Then

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temperature of the gas is decrease

final pressure of the gas is $\frac{{Kx}_{0}}{S}$

change in internal energy of the gas is $\frac{1}{2} {Kx}_{0}^{2}$

work done by the gas is $\frac{1}{2} {Kx}_{0}^{2}$

answer is A, B, C, D.

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Detailed Solution

Equilibrium of piston gives $PS = {Kx}_{0}$

$P = \frac{{Kx}_{0}}{S}$

Since the chamber is thermally insulated, $LΔQ = 0$

$∴$ Elastic PE of spring = Work done by gas

or, Work done by gas $= \frac{1}{2} {Kx}_{0}^{2}$

This work is done at the expense of internal energy of the gas.

Therefore, internal energy of the gas is decreased by $(1 / 2) {Kx}_{0}^{2}$ .

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