Page 85 - Coulson Richardson's Chemical Engineering Vol.6 Chemical Engineering Design 4th Edition

68
CHEMICAL ENGINEERING
Solution
Note: as the data taken from the literature are given in cal/mol the calculation is carried
out in these units and the result converted to SI units.
As no data are given on the exact variation of the C p of the liquid with temperature,
use an equation of the form C p D a C bt, calculating a and b from the data given; this
will be accurate enough over the range of temperature needed.
37.96 24.65
Ž
a D value of C p at 0 C, b D D 0.133
100
78.4 200

2
3
H 200 C D 24.65 C 0.133t dt C 9.22 ð 10 C 14.66 C 3.758 ð 10 t
Ž
0 78.4
5 2
9 3
2.091 ð 10 t C 4.740 ð 10 t dt
78.4 2 3 200 2 2
D [ 24.65t C 0.133t /2] C 9.22 ð 10 C [ 14.66t C 3.758 ð 10 t /2 2.091
0 78.4
5 3
9 4
ð 10 t /3 C 4.740 ð 10 t /4]
3
D 13.95 ð 10 cal/mol
3
3
D 13.95 ð 10 ð 4.18 D 58.31 ð 10 J/mol
Specific enthalpy D 58.31 kJ/mol.
Molecular weight of ethyl alcohol, C 2 H 5 OH D 46
3
Specific enthalpy D 58.31 ð 10 /46 D 1268 kJ/kg
3.6. MEAN HEAT CAPACITIES
The use of mean heat capacities often facilitates the calculation of sensible-heat changes;
mean heat capacity over the temperature range t 1 to t 2 is defined by the following equation:

t 2 t 2
D C p dt ł dt 3.14
C p m
t 1 t 1
Mean specific heat values are tabulated in various handbooks. If the values are for
unit mass, calculated from some standard reference temperature, t r , then the change in
enthalpy between temperatures t 1 and t 2 is given by:

t 1 t r 3.15
H D C p m,t 2 t 2 t r C p m,t 1
were calculated.
where t r is the reference temperature from which the values of C p m
3
2
If C p is expressed as a polynomial of the form: C p D a C bt C ct C dt , then the
integrated form of equation 3.14 will be:
b 2 2 c 3 3 d 4 4
a t t r C t t C t t C t t
r
r
r
D 2 3 4 3.16
C p m
t t r
is required.
where t is the temperature at which C p m