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For a gas obeying the Van der Waals equation (V-bn)(P+an²/V²)=nRT, what is the work done by the system during an isothermal change from volume V₁ to V₂?

1. nRT ln ((V₂-bn)/(V₁-bn))+an² ((V₁-V₂)/(V₁V₂))
2. nRT log₁₀ ((V₂-nβ)/(V₁-nβ))+α n² ((V₁-V₂)/(V₁V₂))
3. nRT ln ((V₂-bn)/(V₁-bn))+β n² ((V₁-V₂)/(V₁V₂))
4. nRT ln ((V₁-bn)/(V₂-bn))+α n² ((V₂-V₁)/(V₁V₂))

Correct answer: nRT ln ((V₂-bn)/(V₁-bn))+an² ((V₁-V₂)/(V₁V₂))

Solution

W = nRT ln((V2-bn)/(V1-bn)) + a n^2 (1/V2 - 1/V1) = nRT ln((V2-bn)/(V1-bn)) + a n^2 ((V1-V2)/(V1 V2)).

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