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Ch_12

Ch_12 - 12 THERMODYNAMIC PROPERTY RELATIONS Develop...

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12. THERMODYNAMIC PROPERTY RELATIONS Develop: Fundamental thermodynamic relations Express properties that cannot be measured directly Maxwell relations Clapeyron Equation Determine enthalpy of vaporization from P, V, T measured values •General relations for dh, du, ds and c p and c v . Methods of evaluations for variations of enthalpy, entropy and internal energy Joule-Thompson coefficient

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Maxwell Relations Means of determining changes in entropy Limited to simple compressible systems s v T v s P T P T P s P v s v T T v s v P s P T v = - = = = - M M
Problem solving Using the Maxwell relations, determine a relation for ( s / P ) T for a gas whose equation of state is P ( v - b ) = RT . Analysis This equation of state can be expressed as Then, From the fourth Maxwell relation P R T P = v P R - = - = P T T P s v b P RT + = v

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Clapeyron Equation Liquid-vapor and solid-vapor phase change- simplified forms. For liquid-vapor phase change, at low pressures: For small temperature intervals, h fg constant For solid-vapor phase change, use enthalpy of sublimation h ig 12 12 fg sat sat fg h h P P T Tv T Tv = = M Derived from Maxwell eqns. Implies a phase change process Constant pressure or Constant temperature g f g fg v v and v v = % 2 fg sat sat h dP dT P R T = 2 1 1 2 1 1 ln fg sat h P P R T T = - % Clapeyron-Clausius Eqn. Variation of saturation P with T
Problem solving Determine the h fg of refrigerant-134a at 50°F on the basis of ( a ) the Clapeyron equation and ( b ) the Clapeyron-Clausius equation. Compare your results to the tabulated h fg value.

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Ch_12 - 12 THERMODYNAMIC PROPERTY RELATIONS Develop...

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