Thermodynamics

For liquid–vapor and solid–vapor phase-change processes atlow pressures, it can be approximated asThe changes in internal energy, enthalpy, and entropy of asimple compressible substance can be expressed in terms ofpressure, specific volume, temperature, and specific heatsalone asdu c v dT c T a 0P0T b P d dvvdh c p dT c v T a 0v0T b d dPPds c v 0PdT aT 0T b dvvorln a P 2b h fgP 1 satds c p 0vdT aT 0T b dPPFor specific heats, we have the following general relations:a 0c v0v b T a 02 PT 0T b 2 va 0c p0P b T a 02 vT 0T b 2 Pc p,T c p0,T T PR a T 2 T 1T 1 T 2c p c v T a 0v 20T b0a 02 v0T b dP2PPbsata 0P0v b Tc p c v vTb2aChapter 12 | 675where b is the volume expansivity and a is the isothermalcompressibility, defined asb 1 v a 0v0T b anda 1Pv a 0v0P b TThe difference c p c v is equal to R for ideal gases and tozero for incompressible substances.The temperature behavior of a fluid during a throttling (h constant) process is described by the Joule-Thomson coefficient,defined asm JT a 0T0P b hThe Joule-Thomson coefficient is a measure of the change intemperature of a substance with pressure during a constantenthalpyprocess, and it can also be expressed asm JT 1 c v T a 0vc p 0T b dPThe enthalpy, internal energy, and entropy changes of real gasescan be determined accurately by utilizing generalized enthalpyor entropy departure charts to account for the deviation fromthe ideal-gas behavior by using the following relations:h 2 h 1 1h 2 h 1 2 ideal R u T cr 1Z h2 Z h12u2 u 1 1h 2 h 1 2 R u 1Z 2 T 2 Z 1 T 1 2s2 s 1 1 s 2 s 12 ideal R u 1Z s2 Z s12where the values of Z h and Z s are determined from the generalizedcharts.REFERENCES AND SUGGESTED READINGS1. G. J. Van Wylen and R. E. Sonntag. Fundamentals ofClassical Thermodynamics. 3rd ed. New York: JohnWiley & Sons, 1985.2. K. Wark and D. E. Richards. Thermodynamics. 6th ed.New York: McGraw-Hill, 1999.PROBLEMS*Partial Derivatives and Associated Relations12–1C Consider the function z(x, y). Plot a differential surfaceon x-y-z coordinates and indicate x, dx, y, dy, (z) x ,(z) y , and dz.12–2C What is the difference between partial differentialsand ordinary differentials?*Problems designated by a “C” are concept questions, and studentsare encouraged to answer them all. Problems designated by an “E”are in English units, and the SI users can ignore them. Problemswith a CD-EES icon are solved using EES, and complete solutionstogether with parametric studies are included on the enclosed DVD.Problems with a computer-EES icon are comprehensive in nature,and are intended to be solved with a computer, preferably using theEES software that accompanies this text.