An equation for Gm of a pure substance as a function of T and P (or of Am as a function of T and V) is called a fundamental equation of state. From a fundamental equation of state, one can calculate all thermodynamic properties of a substance. Express each of the following properties in terms of Gm, T, P, (∂Gm/∂T)P, (∂Gm/∂P)T, (∂2Gm/∂T2)p, (∂2Gm/∂P2)T, and ∂2Gm/∂P∂T. (a) Sm; (b) Vm; (c) Hm, (d) Um, (e) CP,m;(f) C.V,m; (g) α; (h)k [Using Eqs. like (4.60) and (4.63) for ∆H and ∆S and experimental Cp, α, and k data, one can construct a fundamental equation of state of the form Gm = f(T, P), where U and S have each been arbitrarily assigned a value of zero in some reference state, which is usually taken as the liquid at the triple point. Accurate fundamental equations of state have been constructed for several fluids. For fluid H2O, fundamental equations of state contain about 50 parameters whose values are adjusted to give good fits of experimental data; see A. Saul and W.Wagner, J. Phys. Chew. Ref. Data, 18, 1537 (1989); P. G. Hill, ibid, 19, 1233 (1990).]
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