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One mole of a gas is put under a weightl...

One mole of a gas is put under a weightless piston of a vertical cylinder at temperature T. The space over the piston opens into atmosphere. Initially, piston was in equilibrium. How much work should be performed by some external force to increase isothermally the volume under the piston to twice the volume? (Neglect friction of piston).

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Verified by Experts

The correct Answer is:
A, B
`F=p_A=p_0A`
`F=(p_0-p)A`
`W=int_(V)^(2V)(p_0-p)Adx`
`=int_V^(2V)p_0dV-int_V^(2V)pdV`
`=p_0V-int_V^(2V)RT((dV)/(V))`
`=p_0V-RTIn(2)`
`=RT-RTIn(2)`
`=RT(1-In2)`
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