Homework 4, due 2/12 at the beginning of class
1
. The Pitzer method is a common methodology used to improve the accuracy of PVT data
estimates obtained from the compressibility chart
. In this method, an acentric factor , , is
defined as:

1

..is the reduced saturation pressure at a temperature that is 70% of the critical
temperature
. (Values for are tabulated for common fluids in Matsoukas App
. A
.) The
compressibility is then
,
Z0 and Z1 are functions of temperature and pressure but are the same for all substances
(but varies from substance to substance)
. Values for , Z0 and Z1 are tabulated in LeeKesler tables
.(a) Using the LeeKesler tables found in the course website (on ANGEL), calculate the
compressibility factor for water at T = 200 oC and P = 20 bar (20 pts)
(b) Calculate the molar volume using the compressibility factor obtained from (a) (5 pts)
2
. Imagine that you have a 20 m3 tank
. Calculate the temperature if you add 150 kg of water
and apply heat until
(a) P = 10 bar (15 pts)
(b) P = 20 bar (10 pts)
3
. Determine Z and V for steam at 250 oC and 1800 kPa using the following:
(a) Steam tables
. (3 pts)
(b) Truncated virial equation,
1
Pitzer correlation,
(c) Truncated virial equation,
, with the value of B from the generalized
. (10 pts)
1
with the following values for the
virial coefficient:
B = 152
.5 cm3 mol 1
C =  5800 cm6 mol2
(10 pts)
(d) Which is the most accurate one (a, b or c)? (2pts)
4
. (a) For nitrogen, methane, noctane and water, compute the compressibility factor Z at the
critical point, and the reduced triple point pressures P3/Pc and temperatures T3/Tc
. Make a
table of your results
. How different are the values for the four different substances? If the law
of corresponding states were exact, what would you expect to find? (10 pts)
(b) Using the respective tables for saturated R134a (R134a is a commonly used refrigerant)
and water, make a loglog plot the coexistence curve for both substances in reduced units
(P/Pc as a function of V/Vc)
. How is this a test of the law of corresponding states? (15 pts)