n moles of a perfect gas undergo a cyclic process ABCA, shown in the figure, consisting of the following processes. A→ B: isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂=2V₁ and the pressure changes from P₁ to P₂. B→ C: isobaric compression at pressure P₂ back to t…

Question

n moles of a perfect gas undergo a cyclic process ABCA, shown in the figure, consisting of the following processes. A→ B: isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂=2V₁ and the pressure changes from P₁ to P₂. B→ C: isobaric compression at pressure P₂ back to the initial volume V₁. C→ A: isochoric change leading to a change of pressure from P₂ to P₁. The total work done in the complete cycle ABCA is

Accepted Answer

(1) nRT(ln 2-1/2). A to B, isothermal doubling: W_AB=nRT ln 2. B to C, isobaric compression at P₂ from 2V₁ to V₁: W_BC=P₂(V₁-2V₁)=-P₂V₁, and P₂=(nRT)/(2V₁), so W_BC=-(nRT)/2. C to A, isochoric: W_CA=0. W=nRT(ln 2-1/2).

Step-by-step solution

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