tailieunhanh - Lecture Thermodynamics: An engineering approach (8/e): Chapter 12 - Yunus A. Çengel, Michael A. Boles

Chapter 12 - Thermodynamic property relations. 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;. | Chapter 12 Thermodynamic Property Relations Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 8th edition by Yunus A. Çengel and Michael A. Boles 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 | Chapter 12 Thermodynamic Property Relations Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 8th edition by Yunus A. Çengel and Michael A. Boles 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 each other, the terms in each bracket must be zero. Thus, we obtain the reciprocity relation that shows that the inverse of a partial derivative is equal to its reciprocal. or The second relation is called the cyclic relation. Another way to write this last result is The Clapeyron Equation The Clapeyron equation enables us to determine the enthalpy change asso­ciated with a phase change, hfg, from knowledge of P, v, and T data alone. Consider the third Maxwell relation During phase change, the pressure is the saturation pressure, which depends on the temperature only and is independent of the specific volume. That is Psat = f(Tsat). Therefore, the partial derivative can be expressed as a total derivative (dP/dT)sat, which