The final volume (in L) of one mole of an ideal gas initially at 27°C and 8.21 atm pressure, if it absorbs 420 cal of heat during a reversible isothermal expansion, is

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V₁ = nRT/P = (1 × 0.0821 × 300)/8.21 = 3 L. Reversible isothermal: q = W = nRT ln(V₂/V₁). With R = 2 cal K⁻¹ mol⁻¹: 420 = 1 × 2 × 300 × ln(V₂/3) ⇒ ln(V₂/3) = 0.7 ⇒ V₂/3 = e⁰·⁷ ≈ 2, so V₂ = 6 L.

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