tailieunhanh - Lecture Companion site to accompany thermodynamics: An engineering approach (7/e): Chapter 12 - Yunus Çengel, Michael A. Boles
Chapter 12 - Thermodynamic property relations. This chapter develop fundamental relations between commonly encountered thermodynamic properties and express the properties that cannot be measured directly in terms of easily measurable properties. This chapter also review and use partial derivatives in the development of thermodynamic property relations. | Chapter 12 Thermodynamic Property Relations Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 7th edition by Yunus A. Çengel and Michael A. Boles Some thermodynamic properties can be measured directly, but many others cannot. Therefore, it is necessary to develop some relations between these two groups so that the properties that cannot be measured directly can be evaluated. The derivations are based on the fact that properties are point functions, and the state of a simple, compressible system is completely specified by any two independent, intensive properties. Some Mathematical Preliminaries Thermodynamic properties are continuous point functions and have exact differentials. A property of a single component system may be written as general mathematical function z = z(x,y). For instance, this function may be the pressure P = P(T,v). The total differential of z is written as where Taking the partial derivative of M with . | Chapter 12 Thermodynamic Property Relations Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 7th edition by Yunus A. Çengel and Michael A. Boles Some thermodynamic properties can be measured directly, but many others cannot. Therefore, it is necessary to develop some relations between these two groups so that the properties that cannot be measured directly can be evaluated. The derivations are based on the fact that properties are point functions, and the state of a simple, compressible system is completely specified by any two independent, intensive properties. Some Mathematical Preliminaries Thermodynamic properties are continuous point functions and have exact differentials. A property of a single component system may be written as general mathematical function z = z(x,y). For instance, this function may be the pressure P = P(T,v). The total differential of z is written as where Taking the partial derivative of M with respect to y and of N with respect to x yields Since properties are continuous point functions and have exact differentials, the following is true The equations that relate the partial derivatives of properties P, v, T, and s of a simple compressible substance to each other are called the Maxwell relations. They are obtained from the four Gibbs equations. The first two of the Gibbs equations are those resulting from the internal energy u and the enthalpy h. The second two Gibbs equations result from the definitions of the Helmholtz function a and the Gibbs function g defined as Setting the second mixed partial derivatives equal for these four functions yields the Maxwell relations Now we develop two more important relations for partial derivatives—the reciprocity and the cyclic relations. Consider the function z = z(x,y) expressed as x = x(y,z). The total differential of x is Now combine the expressions for dx and dz. Rearranging, Since y and z are independent of .
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