In the P–V diagram, a gas goes A(2V₀,P₀) → B(3V₀,P₀) → C(3V₀,2P₀) → D(2V₀,2P₀) → E(V₀,2P₀). Find the total work done by the gas from A to E.
Options

Question

In the P–V diagram, a gas goes A(2V₀,P₀) → B(3V₀,P₀) → C(3V₀,2P₀) → D(2V₀,2P₀) → E(V₀,2P₀). Find the total work done by the gas from A to E.

G1 Physics · Accepted Answer

Work done equals ∫P dV. A→B: W₁=P₀(3V₀-2V₀)=P₀V₀. B→C is isochoric, so W₂=0. C→E occurs at pressure 2P₀ with volume decreasing from 3V₀ to V₀: W₃=2P₀(V₀-3V₀)=-4P₀V₀. Hence W=W₁+W₂+W₃=-3P₀V₀.