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Unformatted text preview: Chapter 8: Thermodynamics 35 From this one can derive Maxwells 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 denitions 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 =- dA , with the surface tension. From this follows: = U A S = F A T 8.6 Processes The efFciency of a process is given by: = Work done Heat added The Cold factor of a cooling down process is given by: = Cold delivered Work added Reversible adiabatic processes For adiabatic processes holds: W = U 1- U 2 . For reversible adiabatic processes holds Poissons equation:....
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