The Algebra of State Functions. The Helmholtz and Gibbs Functions

Until now, we have encountered four state functions of a system characterized by the measurable variables: absolute pressure, P; absolute temperature, T; and the composition of the system expressed by the number of moles of each compound present, n_i. These state functions are the total volume, V; the internal energy, U; the entropy, S; and the enthalpy, H. Two more state functions are used in thermodynamics. These are the Helmholtz function, 4.1 https://www.w3.org/1998/Math/MathML"> A = U − T S https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315399065/5df30985-80c1-4e11-9533-10c20ed2604c/content/equ04_01.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and the Gibbs function, 4.2 https://www.w3.org/1998/Math/MathML"> G = H − T S https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315399065/5df30985-80c1-4e11-9533-10c20ed2604c/content/equ04_02.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>