One mole of a certain ideal gas is contained under a weightless piston of a vertical cylinder at a t — Thermodynamics and Thermochemistry Chemistry Question
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.
Answer: A
💡 Solution & Explanation
Let the external agent do work $W_{agent}$. Work of gas $W_{gas} = W_{agent} - P_{atm}\Delta V = -RT\ln(n)$. Initial state implies $P_{atm}V_0 = RT$. Substitute $P_{atm}\Delta V = P_{atm}(nV_0 - V_0) = RT(n-1)$. So $W_{agent} = RT(n-1) - RT\ln(n)$.
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