Practice question
Question
Calculate the work done when 1 mol of an ideal gas ( γ = 1.67 ) is compressed adiabatically from 20 L to 4 L at 300 K. ( R = 8.314 J/mol·K )
Explanation
For adiabatic compression, T₂ = T₁ (V₁/V₂)γ⁻¹ = 300 × (20/4)⁰.⁶⁷ ≈ 300 × 2.63 = 789.0 K . Then, Cv = R/(γ-1) = 8.314 / 0.67 ≈ 12.41 J/mol·K . Work done: w = nCvΔ T = 1 × 12.41 × (789.0 - 300) ≈ 6068.3 J .
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