Source: Equations and examples adop
ted from
Smith, J.M
., Van N
ess, H.C. and Abbott, M.M
. Introduction to Chemical Engineering Therm
odynam
ics, 7th Edition, M
cGraw-H
ill, 2005(if not specified
elsewhere)
Chapter 4: H
eat Effects
Heat transfer is com
mon in
chemical industry. C
ombustion, extraction,
distillation etc. involve heat effects that accompany physical a
nd
chem
ical changes with the principle of thermodynam
ics.
1
Objective
�To
apply thermodynam
ics to the evaluation of the heat
effects that accompany physicaland chem
icaloperations
�Sensible heat effects (tem
perature change)
�Latent heat effects (phase transition)
�Heat effects of chem
ical reaction, form
ation, and combustion
under standardconditions as well as actual industrial
under standardconditions as well as actual industrial
conditions
�Heat effects of mixing processes (not treated in this chapter)
2
Sensible Heat Effects
�Relations between quantity of heat transferred and
resulting temperature change
∫=
∆=
2
1T TVdT
CU
QFo
r mechanically reversible, constant-volume,
closed-system processes
1 ∫=
∆=
2
1T TPd
TC
HQ
Sensible heat effects are characterisedby temperature changes in a system in which
there are no phase transitions, no chem
ical reactions, and no changes in composition.
For mechanically reversible, constant-pressure,
closed-system processes / steady-flo
w heat
transfer where
∆EP ,
∆EK ≈0, W
s= 0
3
Heat Capacity: Temperature Dependence
�Ideal-gas heat capacity, rather than actual heat capacity
22
−+
++
=D
TC
TB
TA
RCPig
ig PC
�Ideal-gas heat capacity, rather than actual heat capacity
�More convenient for thermodynam
ic-property evaluation in
two steps:
1.
Calculation for hypothetical ideal-gas-state values
2.
Correction to real-gas values
PC
Param
eters in equation for CPcan be found in App. C
.4
1−
=RC
RCig P
ig V
Relations between the tw
o
ideal-gas heat capacities
5
Heat Capacity: G
as Mixtures
...
++
+=
ig PC
ig PB
ig PA
ig PC
BA
mix
Cy
Cy
Cy
C
ig Pi
ig PC
yC
∑=
Pi
Pi
mix
Cy
C∑
=
In an ideal-gas mixture, the molecules have no influence on one another, and each gas
exists independent of the others.
6
Heat Capacity: Evaluation of the Integral
∫∫
==
∆=
T T
ig PT T
Pd
TRC
Rd
TC
HQ
00
To calculate Q
or
∆H given T
0and T:
Read textbook, Smith et al. (2005) p.130 and Ex. 4.2 for details.
To calculate Q
or
∆H given T
0and T:
7
Heat Capacity: Evaluation of the Integral
To calculate T given T
0and Q
or
∆H (an iteration schem
e is helpful):
Read textbook, Smith et al. (2005) p.130 for details.
()
0T
TC
HH
P−
=∆
()
10
.4
0T
C
HT
HP
+∆
=
1. G
uess T, then
calculate τ, then
substitute into
Eq. (4.8)
2. Substitute
<C
P>Hinto Eq.
(4.10) to get
new
T
3. Substitute new
T into
Eq. (4.8) to reevaluate
<C
P>Huntil iteration
converges.
8
Exercise: Problem 4.2 (a)
�Fo
r steady flo
w through a heat exchanger at
approximately atmospheric pressure, w
hat is the final
temperature,
(a) when heat in the am
ount of 800 kJ is added to 10 m
ol
of ethylene initially at 200
°C (473.15 K)?
9
10
103B = 14.394
B = 14.394 x 10-3
Exercise: Problem 4.2 (a) (cont’d)
Guess T = 400
°C (673.15 K), thus
τ= 2.
()(
)(
)(
)0
12
215
.473
10
392
.4
12
15
.473
10
394
.14
424
.1
22
63
++
+×
−+
+×
+=
−−
CH
P
11
()(
)(
)(
)0
12
215
.473
3
10
392
.4
12
15
.473
2
10
394
.14
424
.1
22
++
+×
−+
+×
+=
R
HP
346
.9
=R
CH
P
0T
C
HT
HP
+∆
=
Latent Heats of Pure Substances
�Phase transition, coexistence of tw
o phases, no
temperature change
�Clapeyronequation (derived in Chapter 6)
dT
dP
VT
Hsa
t
∆=
∆
�Trouton’srule (rough estimates at T
n)
dT
10
≈∆
nn
RTH
12
Latent Heats of Pure Substances
�Riedel equation (high accuracy, error < 5%)
�Watson equation (with a known value, experimental o
r
()
nr
c
nn
T
P
RTH
−−=
∆
93
0.
0
01
3.
1ln
09
2.
1P (bar)
�Watson equation (with a known value, experimental o
r estimated by Riedel equation)
38
.0
12
12
11
−−=
∆∆
rr
TT
HH
13
Standard Heats: R
eaction, Form
ation,
Combustion
�Revision: Read Chapter 4 (4.3-4.5), Sm
ith et al. (2005)
∑∆
≡∆
i
o fii
oH
vH
Positive (+) for products
Negative (–) for reactants
Standard states: pure substance at ideal-gas state at 1 bar, real pure liquid or solid at 1 bar
14
15
Standard Heats: Temperature Dependence
temperature
temperature
temperature
change
temperature
change
chem
ical
reaction
16
Standard Heats: Temperature Dependence
17
Standard Heats: Temperature Dependence
18
Example 4.6: Standard heat at temperature
other than 298.15 K
�Calculate standard heat of methanol-synthesis reaction at
800
°C (1073.15 K):
CO(g) + 2H
2(g) � ���
CH
3OH(g)
19
AA
ii
∆=
∑ν
20
21
Heat Effects of Industrial Reactions
�Industrial reactions are often carried out under/w
ith
�non standard-state conditions
�non stoichiometricproportions
�reaction not go to completion
�variation in tem
perature
presence of inert
�presence of inert
�several reactions simultaneo
usly
22
23
24
Conclusions
�In this chapter, we have evaluated the heat effects that
accompany physicaland chem
icaloperations from the
point of thermodynam
ics.
�We have exam
ined
�Sensible heat effects (as a result of temperature change)
�Latent heat effects (due to phase transition)
�Latent heat effects (due to phase transition)
�Heat effects of chem
ical reaction, form
ation, and combustion
under
�standard conditions
�actual industrial conditions
�Self study
�Read Chapter 4 (Sm
ith et al. 2005)
�Attem
pt Tutorial 3: Problems 4.11, 4.38, 4.49,4.51
25