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CHAPTER 4
Heat Effects
Miss. Rahimah Bt. Othman
Email: [email protected]
ERT 206/4ERT 206/4ThermodynamicsThermodynamics
COURSE OUTCOME 1 CO1)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
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)
Ethylene glycol can be formed readily prepared in the laboratory by refluxing ethylene dichloride with a dilute solution of sodium carbonate (Na2CO3).
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.
Ethylene glycol in 3-DChemical structure of Ethylene glycol
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.
2
1
T
T PdTCHQ
2
1
T
T V dTCU (4.1)Derive:
(4.2)
(4.3)
2
1
T
T PdTCH
Temperature dependence of the Heat Capacity
22 cTbTaR
CandTT
R
C PP
and, and a, b, c = constant characteristic of the particular substance
Exception: ɣT2 = cT-2 (form)
CP/R = A + BT + CT2 + DT-2
or Is = 0dimensionless
Unit of Cp governed by the choice of R
(4.4)
The influence of T on CPig for Ar, N2, H2O and CO2
From Eq 3.19
RCRdT
dU
dT
dHC VP
•Values of parameters are given in Table C.1 pg. 684: Heat capacityof 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.
1R
C
R
C igP
igV (4.5)The 2 ideal-gas heat capacity:
Are related
•The T dependence of Cvig/R follows from the T dependence of CP
ig/R.
• The effect of T on CPig and CV
ig 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 CV
ig ≈ their true heat capacity
• Refer to Exp 4.1
A
B
C A
BC
• 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 Pmixtureig = yACPA
ig + yBCPBig + ycCPC
ig (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 Sensible-Heat Integral
0
0
330
2200
0
1)1(
3)1(
2)1(
T
Twhere
T
DT
CT
BATdT
R
CT
T
P
20
2200 )1(
3)1(
2 T
DT
CT
BA
R
CHP
)( 0TTCHHP
(4.7)
0TC
HT
HP
(4.8)
(4.9)
(4.10)
Refer to Exp. 4.2
• 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 conveniently expressed as; (4.7)
Use of Define Functions
T
T
P JEEICPHRdTR
CQ
0
778,19)0.0,6164.2,3081.9,702.1;15.873,15.533( x
T
T
P DCBATTICPHdTR
C0
),,,;,0(
Computer programming (Maple® / Mathcad® ):
When the quantities in parentheses are assigned numerical value, thus
Refer to App. D (pg.69) for representation of comp. programming
JDCBATTRxMCPHR
CH HP 778,19),,,;,0(
Refer to Exp.4.3
Drawing of an experiment to measure the latent heat of vaporization as steam condenses to water.
4.2 LATENT HEAT OF PURE SUBSTANCE
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.:
dT
dPVTH
sat
(4.11)(Clapeyron Equation)
• 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.
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
10~n
n
RT
H
RIEDEL7
Equation proposed by Riedel: Pc = critical pressure, Trn=reduced T
at Tn.
Accurate for an impirical expression; error rarely >5%
nr
C
n
n
T
P
RT
H
930.0
)013.1(ln092.1 (4.12)
RIEDEL7 (cont…)
Applied to H2O it gives:
How to get Pc & Trn? How to get 2,334 Jg-1 & 2,257 Jg-1?
1065,42)15.373)(314.8)(56.13(,
56.13577.0930.0
)013.15.220(ln092.1
JmolHWhence
RT
H
n
n
nr
c
n
n
T
P
RT
H
930.0
)013.1(ln092.1
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: 38.0
1
2
1
2
1
1
r
r
T
T
H
H(4.13)
(Refer to Exp. 4.4)
STANDARD HEAT OF REACTION, ∆Ho
298
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
igP
oP
C
C Degree symbols = standard state
Ideal gas
Std state of gases = ideal-gas state igP
oP CC
STANDARD HEAT OF FORMATION, ∆HO
f298
A formation reaction = Rxn which form a single compoundsingle 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
i
oii
o HH (4.14)
• Hoi = ∆Ho
f if standard-state enthalpies of all elements are arbitrarily =0
• Eq. 4.14 becomes:
i
ofi
o
iHH (4.15)
i
oPi
oP i
CC (4.16)
dTCHd oP
o (4.17)
• Integration of Eq (4.17) Eq. (4.18)• Integration of Eq (4.4) Eq.(4.19)• Obtaining Eq.4.20 – Eq.4.21
THANK YOU