Berthelot\'s equation of state may be expressed as: At the critical point, Use t

Question

Berthelot's equation of state may be expressed as: At the critical point, Use this fact to derive expressions for a, b and in terms of Perit, Terit and For water, Perit = 221.2bar and Terit = 374-15degreeC. Find a, b and Plot P in bar in the range of obar to 500bar against in m3/kmol in the range of o n/kmol to 0.4 m3/kmol, when T = 620K, 630K, 640K, 647.3K, 660K, 670K and 680K. Finally, express the compressibility factor Z in terms of the reduced temperature and the pseudo-reduced specific volume VR.

Explanation / Answer

All the following P, T, v should have subscript crit.

P = RT/(v - b) - a/(Tv2) (1)

(P/v)T = -RT/(v - b)2 + 2a/(Tv3) = 0, so RT2v3 = 2a(v - b)2   (2)   

(2P/v2)T = 2RT/(v - b)3 - 6a/(Tv4) = 0, so 2RT2v4 = 6a(v - b)3   (3)

(3)/(2): 2v = 3(v - b), so b = v/3

a = RT2v3/(v - b)2 = 9RT2v/8

use (1), we get P = 3RT/(8v), so

v = 3RT/(8P), a = 27R2T3/(64P), b = RT/(8p)

For P = 221.2 bar = 2.212*107 Pa, T = 374.15 oC = 647.3 K, R = 8.314*103 Pa-m3/(kmol-K)

so v = 0.0912 m3/kmol, a = 3.57*108 Pa(m3/kmol)2K, b = 0.0304 m3/kmol

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