Question 6.9: Estimate V, U, H, and S for 1-butene vapor at 200°C and 70 b...
Estimate V, U, H, and S for 1-butene vapor at 200°C and 70 bar if H and S are set equal to zero for saturated liquid at 0°C. Assume that the only data available are:
T_{c} = 420.0 K P_{c} = 40.43 bar ω = 0.191
T_{n} = 266.9 K ( normal boiling point )
C_P^{ig} / R=1.967+31.630 \times 10^{-3} T-9.837 \times 10^{-6} T^2 \quad (T K)
The volume of 1-butene vapor at 200°C and 70 bar is calculated directly from the equation V = ZRT/P, where Z is given by Eq. (3.53) with values of Z^0 and Z^1 interpolated in Tables D.3 and D.4. For the reduced conditions,
Z = Z^0 + ω Z^1 (3.53)
T_r=\frac{200+273.15}{420.00}=1.127 \quad P_r=\frac{70}{40.43}=1.731
the compressibility factor and molar volume are:
Z = Z^0 + ω Z^1 = 0.485 + ( 0.191 ) ( 0.142 ) = 0.512
V=\frac{Z R T}{P}=\frac{(0.512)(83.14)(473.15)}{70}=287.8 \mathrm{~cm}^3 \cdot \mathrm{mol}^{-1}
For H and S, we use a computational path like that of Fig. 6.3, leading from an initial state of saturated liquid 1-butene at 0°C, where H and S are zero, to the final state of interest. In this case, an initial vaporization step is required, leading to the four-step path shown by Fig. 6.4. The steps are:
(a) Vaporization at T_1 and P_1 = Psat.
(b) Transition to the ideal-gas state at (T_1, P_1).
(c) Change to (T_2, P_2) in the ideal-gas state.
(d) Transition to the actual final state at (T_2, P_2).
