- 22 Consider A Fluid Near Its Critical Point With Isotherms As Sketched In Figure 12 3 Assume That The Singular Part O 1 (62.94 KiB) Viewed 24 times
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22. Consider a fluid near its critical point, with isotherms as sketched in Figure 12.3. Assume that the singular part of the Gibbs free energy of the fluid is of the form Gº (T,P) |t2-g(/1t|4), where 1 = (P-P)/Pc, t= (T - Te)/Te while g(x) is a universal function, with branches gt for t> 0 and g-for t < 0; in the latter case, the function g- has a point of infinite curvature at a value of that varies smoothly with t, such that (0) = 0 and (3A/at)1-0 =const. (a) Using the above expression for Gø, determine the manner in which the densities, p, and pg, of the two phases approach one another as t+ 0 from below. (b) Also determine how (P-Pc) varies with (p - Pe) as the critical point is approached along the critical isotherm (t = 0). (c) Examine as well the critical behavior of the isothermal compressibility Kt, the adiabatic compressibility ks, the specific heats Cp and Cy, the coefficient of volume expansion ap, and the latent heat of vaporization l. 23. Consider a model equation of state which, near the critical point, can be written as ham(t+bm?) (1<< 2;a, b>0). Determine the critical exponents B, y, and 8 of this model, and check that they obey the scaling relation (12.10.22). 24 Athaba latinti tinglarba dieta chou