Two moles of an ideal gas are contained under a weightless piston of a vertical cylinder at a temperature T. The space over the piston opens into the atmosphere. What work has to be performed in order

Question

Two moles of an ideal gas are contained under a weightless piston of a vertical cylinder at a temperature T. The space over the piston opens into the atmosphere. What work has to be performed in order to increase isothermally the gas volume under the piston k times by slowly raising the piston? The friction of the piston against the cylinder walls is negligibly small.

TestHub · Accepted Answer

The weightless piston means the initial gas pressure equals P atm , so P atm V 1 = 2RT. Work by the agent = ∫(P atm - P gas )dV = P atm (k-1)V 1 - 2RTln k = 2RT(k - 1) - 2RTln k = 2RT(k - 1 - ln k). Matches (c).

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