A thermodynamic system undergoes cyclic process ABCDA as shown in the P–V figure. A = (V₀, P₀), B = (2V₀,3P₀), C = (V₀,3P₀), D = (2V₀, P₀), connected in the order A → B → C → D → A. The work done by the system over one full cycle is:
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Question

A thermodynamic system undergoes cyclic process ABCDA as shown in the P–V figure. A = (V₀, P₀), B = (2V₀,3P₀), C = (V₀,3P₀), D = (2V₀, P₀), connected in the order A → B → C → D → A. The work done by the system over one full cycle is:

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G1 Physics · Accepted Answer

Step 1: Work done around a full P–V cycle is the algebraic sum of ∫P dV along all four paths. Step 2: Along A→B, volume increases by V₀ and pressure rises linearly from P₀ to 3P₀. The work for this path is [(P₀ + 3P₀)/2]V₀ = +2P₀V₀. Step 3: Along B→C, pressure is 3P₀ while volume decreases by V₀; W = −3P₀V₀. Step 4: Along C→D, volume increases by V₀ and pressure decreases linearly from 3P₀ to P₀; W = +2P₀V₀. Step 5: Along D→A, pressure is P₀ and volume decreases by V₀; W = −P₀V₀. Step 6: Net wo…

A thermodynamic system undergoes cyclic process ABCDA as shown in the P–V figure. A = (V₀,P₀), B = (2V₀,3P₀), C = (V₀,3P₀), D = (2V₀,P₀), connected in the order A → B → C → D → A. The work done by the system over one full cycle is: