By Frank Weinhold
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4 REAL AND IDEAL GASES 45 (since Vm21 ! 0, or Vm ! 1, as P ! 0). 29) as the infinite power series Z(Vm , T) ¼ 1 þ B(T) 1 Vm þ C(T) 3 1 2 1 þ D(T) þÁÁÁ Vm Vm (2:30) Here B(T ) is the second virial coefficient, C(T ) the third virial coefficient, and so forth. 30) is expected to achieve useful accurary with only a few terms. Higher densities within the domain of convergence require additional terms to achieve a desired accuracy. For some densities, the virial series may not converge at all.
0 since Vm ! (Vm)ideal as P ! 0. Thus, measured values of Z carry information about deviations from ideal gas behavior at nonzero pressures. Let us first examine the pressure dependence of the compressibility factor under isothermal conditions. 2 and Fig. 2 exhibit some representative P-dependent values of Z for gaseous CO2 (at fixed temperature 408C ¼ 313K) in tabular and graphical form. 2 P-dependent compressibility factor Z for CO2 (a) over a broad pressure range at 408C, and (b) compared with other gases in a narrower low-pressure range at 08C.
8) allows B(T ) to be explicitly evaluated by statistical mechanical methods as 1 ðh i B(T) ¼ 2pNA 1 À eÀV(R)=kT R2 dR (2:32) 0 Although we shall not pursue such specific molecular formulas in the present thermodynamic exposition, they form the basis for modern molecular-level understanding of gases and liquids [J. O. Hirschfelder, C. F. Curtiss, and R. B. 30) has deeper fundamental significance than other proposed equations of state. The leading correction to ideality arises from the second virial coefficient B(T ), whose qualitative T dependence is shown in Fig.