Compound X enters a steady state compressor as a gas at P1=0.5 bar and T1=300 K, and leaves the compressor at P2=15 bar and T2=600 K. (These are the actual temperature and pressure of the exiting stream.) Then it enters a steady state heat exchanger in which it is cooled and condensed into a liquid at P3=15 bar and T3=200 K.

Question

X has the following properties:
Critical temperature T=250 K
Critical pressure P=40 bar
Acentric factor ?=0.2
Ideal gas heat capacity CP* = 5R
At temperatures equal to or below 250 K, it can be modeled using the Peng-Robinson EOS
At pressures below 1 bar, it can be modeled as an ideal gas
At the conditions of the compressor outlet (2), it can be modeled using the following EOS:
PV = RT + (BP3)

Where B = -4 cm3mol-1bar-2

Prove that ((??H)/?P)_T= ?V- T((??V)/?T)_P
Find a general algebraic expression for the residual molar enthalpy HR, in terms of P, V , T and/or constants, that results from the equation of state PV = RT + (BP3).
Find the change in molar enthalpy for the gas as it goes through the compressor (H2-H1).
Determine the Peng-Robinson parameters a and b for this compound at a temperature of 200 K.
The three solutions of the Peng-Robinson for V at T=200 K and P=15 bar are V = 60.2, 326.3 and 681.6 cm3/mol. Determine the compressibility factor Z for the liquid leaving the heat exchanger.
Suppose you wanted to use the Lee-Kesler method, rather than the Peng-Robinson equation, to model the liquid leaving the heat exchanger (T3, P3). Use the figures in Chapter 7 to estimate the residual molar entropy S3R of this liquid.
Y is another compound in the same chemical family as X. Y has a critical temperature of 300 K and a critical pressure of 30 bar. At what temperature and pressure would you expect compound Y to have a compressibility factor (Z) identical to the one you calculated in part E?

Answer 1

E) Of the three solutions to the Peng-Robinson equation given, 60.2 cm3/mol is the value for the liquid molar volume because it is the smallest of the three.





Using Figures 7-18 and 7-19:



G) Apply principle of corresponding states: