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154 Chapter 5 We can also express H as a function of V and T, in which case the total derivative d H is Because the coefficients of dV and dT in both expressions for dH are equal, we can write and (c) Substituting U + PV for H into the left side of Equation gives = P Using the definitions of Cₚ and (Equations 5.39 and 5.40), this expression becomes C = which is the desired result. 5-29. Starting with H = U + PV, show that = Interpret this result physically. Take the partial derivative of both sides of this equation with respect to T, holding P constant, and substitute Cₚ for H = U + PV + This expression tells us how the total energy of a constant-pressure system changes with respect to temperature. Recall that for a constant pressure process, dH = δq. Then Cₚ = Because dU = δq + δw, the work involved in the process must be - The equation above is equivalent to the statement