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cen84959_ch12

# cen84959_ch12 - cen84959_ch12.qxd 6:03 AM Page 669 Chapter...

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Chapter 12 THERMODYNAMIC PROPERTY RELATIONS | 669 I n the preceding chapters we made extensive use of the property tables. We tend to take the property tables for granted, but thermodynamic laws and principles are of little use to engineers without them. In this chapter, we focus our attention on how the property tables are prepared and how some unknown properties can be determined from limited available data. It will come as no surprise that some properties such as temperature, pressure, volume, and mass can be measured directly. Other properties such as density and specific volume can be determined from these using some simple relations. However, properties such as internal energy, enthalpy, and entropy are not so easy to determine because they cannot be measured directly or related to easily measurable properties through some simple relations. Therefore, it is essential that we develop some fundamental relations between commonly encountered thermodynamic properties and express the properties that cannot be measured directly in terms of easily measurable properties. By the nature of the material, this chapter makes extensive use of partial derivatives. Therefore, we start by reviewing them. Then we develop the Maxwell relations, which form the basis for many thermodynamic relations. Next we discuss the Clapeyron equation, which enables us to determine the enthalpy of vaporization from P , v , and T measurements alone, and we develop general relations for c v , c p , du , dh , and ds that are valid for all pure substances under all condi- tions. Then we discuss the Joule-Thomson coefficient, which is a measure of the temperature change with pressure during a throttling process. Finally, we develop a method of evaluat- ing the h , u , and s of real gases through the use of gen- eralized enthalpy and entropy departure charts. Objectives The objectives of Chapter 12 are to: Develop fundamental relations between commonly encountered thermodynamic properties and express the properties that cannot be measured directly in terms of easily measurable properties. Develop the Maxwell relations, which form the basis for many thermodynamic relations. Develop the Clapeyron equation and determine the enthalpy of vaporization from P , v , and T measurements alone. Develop general relations for c v , c p , du , dh , and ds that are valid for all pure substances. Discuss the Joule-Thomson coefficient. Develop a method of evaluating the h , u , and s of real gases through the use of generalized enthalpy and entropy departure charts.

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12–1 A LITTLE MATH—PARTIAL DERIVATIVES AND ASSOCIATED RELATIONS Many of the expressions developed in this chapter are based on the state pos- tulate, which expresses that the state of a simple, compressible substance is completely specified by any two independent, intensive properties. All other properties at that state can be expressed in terms of those two properties.
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