On page 200 in the 7th edition of Intro to ChemE Thermodynamics by Smith, Van Ness, and Abbott, there is an equation that has always bugged me since reading it (or rather the interpretation of it, not the derivation). It is equation 6.1 and states: d(nU) = T d(nS) - P d(nV)with n = moles in the system, U = molar internal energy, T = temp, S = molar entropy, P = pressure, and V = molar volume. This equation was simply derived from the 1st law assuming a reversible process for the work and heat terms. Then, it goes on to state that this eqn was "derived for the special case of a reversible process. However, it contains only properties of the system...Therefore, it is not restricted in application to only reversible processes..." There is some other filler info that you should read too, but I've quoted the main message. My question is, how can this reasoning make more sense to me? It seems like a big leap of faith to assume that something derived from a specific process (a reversible one) can then be applied to any process (even irreversible ones) just by stating the claim that it only involves state variables. I totally understand what a state variable is, but this doesn't help my acceptance of this idea. Please help! UPDATE: As an example, on page 74 eqn 3.20a: dU = Cv dTwas totally derived for only an ideal gas, however, I see only thermodynamic state properties appearing in this equation, so why is it wrong to assume here that this eqn only can be applied to an ideal gas, whereas 6.1 can be unrestricted from the assumptions under which it was derived. I hope you see my confusion in the analogy.