ECHE 311/SPRING 2015
Problem Set #6
Solution Thermodynamics Theory
1. What is the change of entropy when 0.7 m3 of CO2 and 0.3 m3 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:
S  S ig   xi Si ig   R  xi ln xi
i
2
i
For a particular binary liquid solution at constant T and P, the molar enthalpies of
mixtures are represented by the equation
where
H  x1 (a1  b1x1 )  x2 (a2  b2 x2 )
a1 and b1 are constants. Since the equation has the form
of Eq.

M   xi M i
i
it might be that
_
H 1  a1  b1 x 1
H1
and
H 2  a2  b2 x 2


Derive expression for
_
and
H2
1
to show whether this is true.
3
From the data of steam tables, determine an estimate for f / f
water at 150oC and 150 bar, where f
150oC.
Hint: Use Table F.1 150 oC and Eq:
ln
4
sat
sat
for liquid
is the fugacity of saturated liquid at
V l ( P  Pisat )
 i
f sat
RT
fi
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.
Hint: Use Table F.2, 9000 kPa & 400oC and get the values of H1 and S1.
Use Table F.2, 300 kPa & 400oC and get the values of H2 and S2
The equation
1 H i  H i*
ln
 [
 ( S i  S i* ] may be recast for
*
R
T
fi
this problem.
fi
5
From the following compressibility-factor data for CO2 at 150oC 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:
  exp[
Pr o
( B    B1 )
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
6
For SO2 at 600oK 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 ) .
3