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phys documents (dragged) 41

phys documents (dragged) 41 - Chapter 8 Thermodynamics 35...

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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 definitions of C V and C p it can be derived that: T dS = C V dT + T p T V dV and T dS = C p dT - T V T p dp For an ideal gas also holds: S m = C V ln T T 0 + R ln V V 0 + S m 0 and S m = C p ln T T 0 - R ln p p 0 + S m 0 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 efficiency 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: with γ = C p /C V one gets that pV γ = constant. Also holds: T V γ -
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