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One mole of an ideal gas is contained under a weightless conducting piston in a vertical cylinder at a temperature T. The space over the piston is open to the atmosphere. The amount of work that has to be done to increase the gas volume in the cylinder to n times by slowly raising the piston is (Neglect friction)

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$\frac{RT}{2} [(n-1) - l n (n)]$

$RT [(n-1) - l n (n)]$

$R T [(n-1) - \frac{l n (n)}{2}]$

$\frac{RT}{2} [(n-1) - \frac{l n (n)}{2}]$

answer is A.

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Detailed Solution

Work-Energy theorem
$W_{a t m} + W_{g a s} + W_{e x t} = Δ K . E . = 0$
$W_{e x t} = - W_{a t m} - W_{g a s}$
$W_{a t m} = \int_{V_{0}}^{n V_{0}} P_{0} d V = - P_{0} V_{0} (n - 1)$ and $W_{g a s} = \int_{V_{0}}^{n V_{0}} P d V = R T \ln (n)$

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