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