Solution Thermodynamics Theory

ECHE 311/SPRING 2010 Problem Set #6 Solution Thermodynamics Theory Due Saturday, February 27th

3 3 1. What is the change of entropy when 0.7 m of CO2 and 0.3 m of N2, each at 1 bar and 25oC blend to form a homogeneous gas mixture at the same conditions? Assume ideal gases. The entropy change of mixing is given by Eq:

ig ig S  S  xi S i   R  x iln x i i i

2 For a particular binary liquid solution at constant T and P, the molar enthalpies of mixtures are represented by the equation

H  x1(a1  b1x1)  x2 (a2  b2x2 ) where a1 and b1 are constants. Since the equation has the form of Eq.

M   xi M i i

it might be that

_ _ and H 1 a1  b1x1 H 2  a2  b2x2

  Derive expression for and to show whether this is true. H1 H2

1 3 From the data of steam tables, determine an estimate for f/ f sat for liquid water at 150oC and 150 bar, where f sat is the fugacity of saturated liquid at 150oC. Hint: Use Table F.1 150 oC and Eq:

f V l (P  P sat ) ln i  i i fsat RT

4 Steam at 9,000 kPa and 400oC undergoes an isothermal change of state to a pressure of 300 kPa. Determine the ratio of the fugacity in the final state to that in the initial state. o Hint: Use Table F.2, 9000 kPa & 400 C and get the values of H1 and S1. o Use Table F.2, 300 kPa & 400 C and get the values of H2 and S2 The equation

* f 1 H  H * ln i  [ i i  (S  S ] may be recast for * R T i i fi this problem.

o 5 From the following compressibility-factor data for CO2 at 150 C prepare plots of the fugacity and fugacity coefficient of CO2 vs P for pressures up to 500 bar. Compare the resulting curves with those found from the generalized correlation represented by Eq:

Pr o 1   exp[ (B    B ) Tr

______

P/bar Z P/bar Z ______

10 0.985 100 0.869 20 0.970 200 0.765 40 0.942 300 0.762 60 0.913 400 0.824 80 0.885 500 0.910 ______

2 o 6 For SO2 at 600 K and 300 bar, determine good estimates of the fugacity and of G/RT. Hint: For given conditions the Lee/Kesler correlation is appropriate. Use data from Tables E.15 & E.16. and Eq.   ( o )(1) .