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Question

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 in part B there is vacuum. A massless spring of force constant k is connected with piston and the wall of the container as shown. Initially spring is unstretched. Gas in chamber A is allowed to expand. Consider the compression in spring to be x0 in equilibrium.


A

Final pressure of the gas is kx02s

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B

Work done by the gas is kx20

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C

Change in internal energy of the gas is 12kx20

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D

Temperature of the gas is increased

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Solution

The correct option is C

Change in internal energy of the gas is 12kx20


Analysing equilibrium of piston,

PS=kx0

P=kx0S

Since, the chamber is thermally insulated,

ΔQ=0

Elastic potential energy of the spring

=12kx20

= work done by the gas

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

Therefore, internal energy of the gas is decreased by 12kx20


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