In this note we provide proofs of the following statements for a compressible Newtonian fluid: (i) internal energy being a convex function of entropy and specific volume is equivalent to nonnegativity of both specific heat at constant volume and isothermal bulk modulus; (ii) convexity of internal energy together with the second law of thermodynamics imply linear stability of the rest state; and (iii) linear stability of the rest state together with the second law imply convexity of internal energy.
Keywords:flow instability, entropy, density, specific heat, elastic moduli, compressible flow, equations of state
Topics:Entropy, Fluids, Internal energy (Physics), Stability, Specific heat
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