One mole of a certain ideal gas is 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

Question

One mole of a certain ideal gas is 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 n times by slowly raising the piston? The friction of the piston against the cylinder walls is negligibly small.

TestHub · Accepted Answer

The piston is weightless, so initially the gas pressure equals atmospheric P atm and P atm V 1 = RT. The agent's force supports the difference: work by agent = work done on the piston against (atmosphere minus gas) = ∫ (P atm - P gas )dV = P atm (nV 1 - V 1 ) - RTln n = RT(n - 1) - RTln n. Matches (a).

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