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Unformatted text preview: Chapter 8: Thermodynamics 35 From this one can derive Maxwell’s relations: ∂ T ∂ V S = ∂ p ∂ S V , ∂ T ∂ p S = ∂ V ∂ S p , ∂ p ∂ T V = ∂ S ∂ V T , ∂ V ∂ T p = ∂ S ∂ p T From the total differential and the de¡nitions of C V and C p it can be derived that: TdS = C V dT + T ∂ p ∂ T V dV and TdS = C p dT T ∂ V ∂ T p dp For an ideal gas also holds: S m = C V ln T T + R ln V V + S m and S m = C p ln T T R ln p p + S m Helmholtz’ equations are: ∂ U ∂ V T = T ∂ p ∂ T V p , ∂ H ∂ p T = V T ∂ V ∂ T p for an enlarged surface holds: d W rev = γ dA , with γ the surface tension. From this follows: γ = ∂ U ∂ A S = ∂ F ∂ A T 8.6 Processes The efFciency η of a process is given by: η = Work done Heat added The Cold factor ξ of a cooling down process is given by: ξ = Cold delivered Work added Reversible adiabatic processes For adiabatic processes holds: W = U 1 U 2 . For reversible adiabatic processes holds Poisson’s equation:....
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This note was uploaded on 11/16/2010 for the course ENGR 201 taught by Professor Elder during the Spring '10 term at Blinn College.
 Spring '10
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 Dynamics

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