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Show that for an ideal gas cp-cv=r |
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Answer» Cv = Heat capacity at constant volume. Cp = Heat capacity at constant pressure. q, at constant volume qv = CvΔT = ΔU ...(I) at constant volume qp = CpΔT = ΔH ....(II) We know that — for one mole ideal gas — ΔH = ΔU + Δ(PV) = ΔU + Δ(RT) = ΔU + RΔT (R = constant) ΔH = ΔU + RΔT ΔH - ΔU = RΔT ....(III) Subtracting equation (I) from equation (II) — ΔH - ΔU = CpΔT - CvΔT ....(IV) from equation (III) and (IV) — CpΔT - CvΔT = RΔT Cp - Cv = R |
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