ERT 206/4
Thermodynamics
CHAPTER 4
Heat Effects
Miss. Rahimah Bt. Othman
Email: rahimah@unimap.edu.my
COURSE OUTCOME 1 CO1)
1. Chapter 1: Introduction to Thermodynamics
2. Chapter 2: The First Law and Other Basic Concepts
3. Chapter 3: Volumetric properties of pure fluids
4. Chapter 4: Heat effects
IDENTIFY, REPEAT and ANALYZE sensible heat effects,
latent heat of pure substances, standard heat of reaction,
standard heat of formation, standard heat of combustion,
temperature dependence of ΔH0.
5. Chapter 5: Second law of thermodynamics
6. Chapter 6: Thermodynamics properties of fluids
INTRODUCTION of HEAT
TANSFER
Chemical structure of Ethylene glycol
Ethylene glycol in 3-D
 Ethylene glycol can be formed readily prepared in the laboratory by refluxing
ethylene dichloride with a dilute solution of sodium carbonate (Na2CO3).
 A commercial method for preparing ethylene glycol involves the oxidation
of ethylene to ethylene oxide and the subsequent hydrolysis of this oxide,
over a silver catalyst at 250 degC to ethylene glycol. The reactants, ethylene and
air are heated before entering the reactor. (T will be manipulated for product
optimization)
 The three membered ring in ethylene oxide which is initially in the reaction,
is very reactive. Ethylene oxide readily reacts with water to yield ethylene glycol
or with ammonia to give ethanolamine.
 In this chapter we apply thermodynamics to the evaluation of most of the
heat effects that accompany physical and chemical operations.
4.1 SENSIBLE HEAT EFFECTS

Heat transfer  system (x phase transition, x
chemical rxn & x ∆composition) causes the
∆T of the system only.
Derive:
T2
U   CV dT
(4.1)
T1
T2
H   C P dT
(4.2)
T1
T2
Q  H   C P dT
T1
(4.3)
Temperature dependence of
the Heat Capacity
CP
   T  T 2
R
 ,  and 
and
CP
 a  bT  cT  2
R
and a, b, c = constant characteristic of the particular substance
Exception: ɣT2 = cT-2 (form)
dimensionless
or
CP/R = A + BT + CT2 + DT-2
Unit of Cp governed by the choice of R
Is = 0
(4.4)
The influence of T on CPig for Ar, N2, H2O and CO2
•Values of parameters are given in Table C.1 pg. 684: Heat capacity
of gases in the Ideal Gas state for a number of common organic and
Inorganic gases.
•>accurate but > complx eq are found in the literature
Fluid phase equilibria.
From Eq 3.19
CP 
dH dU

 R  CV  R
dT dT
The 2 ideal-gas heat capacity:
Are related
CVig CPig

1
R
R
(4.5)
•The T dependence of Cvig/R follows from the T dependence of CPig/R.
• The effect of T on CPig and CVig are determined by experiment.
• Reid, Prausnitz and Poling method applied where exp. data are not available.
• Ideal gas heat capacities = real gases (only at P=0); departure of real gases
from ideality is seldom significant at P<several bars.
• At this condition, CPig and CVig ≈ their true heat capacity
• Refer to Exp 4.1
A
C
B
C
A
B
• Gas mixture at CONSTANT composition BEHAVE
= Pure Gases
• In an ID mixture the molecules have x influence on
1 another (independent of the other)
• CPmiixig = Sum of a mixture in the ID state
C
Pmixture
ig
= yACPAig + yBCPBig + ycCPCig
(4.6)
• Heat capacity of solid and liquid also found by experiment.
• Parameters for the T dependence of CP as in Eq 4.4 are given for a few
solids and liquids in Tables C.2 and C.3 of App. C.
• Correlations for the C of many solids and liquids are given by PERRY and
GREEN and by DAUBERT et al.
Evaluation of the SensibleHeat Integral
• Evaluation of the integral is accomplished by substitution for Cp as a function of T,
followed by formal integration. For temperature limitsof T0 and T the result is
(4.7)
conveniently expressed as;

T
T0
CP
B
C
D   1 
dT  AT0 (  1)  T02 ( 2  1)  T03 ( 3  1) 


R
2
3
T0   
where
 
CP
R
H
T
T0
 A
H  CP
T 
(4.7)
H
B
C
D
T0 (  1)  T02 ( 2    1)  2
2
3
T0
(T  T0 )
H
 T0
CP H
Refer to Exp. 4.2
(4.8)
(4.9)
(4.10)
Use of Define Functions
Computer programming (Maple® / Mathcad® ):
CP
T0 R dT  ICPH (T 0, T ; A, B, C , D)
T
When the quantities in parentheses are assigned numerical value, thus
CP
dT  R x ICPH (533.15,873.15;1.702,9.081E  3,2.164 E  6,0.0)  19,778 J
T0 R
Q
T
Refer to App. D (pg.69) for representation of comp. programming
H 
CP
H
R
Refer to Exp.4.3
 RxMCPH (T 0, T ; A, B, C , D)  19,778 J
4.2 LATENT HEAT OF PURE
SUBSTANCE
Drawing of an experiment to measure the latent heat of vaporization as steam
condenses to water.
PHASE RULE : 2-phase system consisting of a single species is univariant, and
its intensive state is determined by the specification of just 1 intensive
property. Thus the latent heat accompanying a phase is a function
of T only, and is related to other system properties by an exact
thermodynamics eq.:
(Clapeyron Equation)
dP sat
H  T V
dT
(4.11)
• Applying Eq. 4.11 to the vaporization of pure liquid, dPsat/dt is the slope
of vapor pressure vs T curve at the T of interest
• ∆V = difference between molar volumes of saturated vapor and
saturated liquid
• ∆H = latent heat of vaporization (calculated from vapor pressure &
volumetric data / measured calorimetrically) – Video clip (exp 3)
• Heat of Vaporization are by far the most important, they have received
more attention.
• 1 procedure of a group-contribution method = UNIVAP6 . Alternative
methods serve 1 of 2 purposes:
Prediction of the heat of vaporization at the normal boiling point
i.e., at a pressure of 1 std atm, define as 101.325 Pa.
Estimation of the heat of vaporization at any T from the known
value at a single T.
Trouton’s Rule




Rough estimation of latent heat of vaporization
for pure liquid at their normal boiling point.
H n
~ 10
RTn
where Tn=Tabs of normal boiling point
∆Hn/RTn = dimensionless
Exprmt. Value: Ar=8.0;N2=8.7; O2=9.1;
HCl=10.4; C6H6=10.5; H2S=10.6; H2O=13.1
RIEDEL7


Equation proposed by Riedel:
Pc = critical pressure, Trn=reduced T at
Tn.
H n 1.092(ln PC  1.013)

RTn
0.930  Trn

(4.12)
Accurate for an impirical expression;
error rarely >5%
RIEDEL7 (cont…)
H n 1.092(ln Pc  1.013)

RTn
0.930  Trn

Applied to H2O it gives:
H n 1.092(ln 220.5  1.013)

 13.56
RTn
0.930  0.577
Whence, H  (13.56)(8.314)(373.15)  42,065 Jmol 1


How to get Pc & Trn?
How to get 2,334 Jg-1 & 2,257 Jg-1?
WATSON8


Estimate the Latent Heat of vaporization of
a pure liquid at ANY T from KNOWN value
at a single T may be based on experimental
value or on a value estimated by Eq.4.12
Wide acceptance:
H 2  1  Tr2

H1  1  Tr1
(Refer to Exp. 4.4)




0.38
(4.13)
STANDARD HEAT OF
REACTION, ∆Ho298





Heat with a specific chemical rxn
depends on the T of both Reactant &
Products.
aA + bB  lL + mM
What is a Standard State?
Gases: Ideal Gas state at 1 bar
Liquid & Solid: Real pure liquid @ Solid
at 1 bar
Symbols
C
o
P
C
ig
P
Degree symbols = standard state
Ideal gas
Std state of gases = ideal-gas state
 CPo  CPig
STANDARD HEAT OF
FORMATION, ∆HOf298



A formation reaction = Rxn which form
a single compound form its constituent
element
f = heat of formation
Refer to Table C.4: Std H & G of
formation at 298.15K
STANDARD HEAT OF
COMBUSTION,


Many ∆Hof298 comes from Std Heat of
Combustion, measured calorimetrically.
Data always based on 1 mol of the
substance burned.
TEMPERATURE DEPENDENCE
OF ∆Ho






General chemical reaction;
lv1lA1 + lv2lA2+…lv3lA3 + lv4lA4+…
lvil=stoiciometric coefficient
Ai = Chemical formula
Species (left) = Reactant
Species (Right)= Product
(+) for PRODUCT & (-) for REACTANT
H o   i H io
i
(4.14)
• Hoi = ∆Hof if standard-state enthalpies of all elements are arbitrarily
=0
• Eq. 4.14 becomes:
H o   i H ofi
(4.15)
i
CPo   i CPoi
(4.16)
i
dH o  CPo dT
• Integration of Eq (4.17)  Eq. (4.18)
• Integration of Eq (4.4)  Eq.(4.19)
• Obtaining Eq.4.20 – Eq.4.21
(4.17)
THANK YOU