# Jacobian - ME 416 Computer Assisted Design of Thermal...

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ME 416 Computer Assisted Design of Thermal Systems Reduction and Evaluation of Thermodynamics Partial Derivatives Reduction Process: Will produce a relationship for a thermodynamic derivative that only depends on T, P, v, κ T , β , and c P . Note that the reduction is completely general and does not depend on the substance. Evaluation Process: Uses the reduced form for the thermodynamic partial derivative with the equations of state for the substance of interest to produce a relationship with only T and P (perhaps c P ) present. Basic Definitions Specific heat at constant pressure: c = T s T P P Thermal expansion coefficient: β = 1 v v T P Isothermal compressibility: κ T T = - 1 v v P Defining Differential Equations Internal energy: du = Tds - Pdv Enthalpy: dh = Tds + vdP Gibbs function: dg = -sdT + vdP Helmholtz function: d ψ = -sdT - Pdv

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Base First Order Derivatives s T = c T
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## This note was uploaded on 07/25/2008 for the course ME 416 taught by Professor Somerton during the Fall '07 term at Michigan State University.

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Jacobian - ME 416 Computer Assisted Design of Thermal...

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