I'm struggling to understand a concept which I assume is basic, but I can't seem to fit the pieces together. When speaking about an ideal gas, I understand that ΔH = ΔU + Δ(PV) = ΔU + RΔT So far so good. I also understand the relationship: ΔU = Q + W... (W here is work being done on the system) In an adiabatic reversible process, Q = 0, which also makes sense. So, W = ΔU = nCvΔT Now, where my confusion lies is in the next part. My book works out a problem, and says: ΔH = W = nCpΔT How can both ΔU and ΔH equal W? This doesn't make sense to me, unless Δ(PV) from the first equation was 0. I don't see how this could be 0 unless we were talking about an isothermal case. It also doesn't make sense because W can't equal both nCvΔT and nCpΔT simultaneously, since Cp = Cv + R. Am I missing something?