CHAPTER 4

Heat Effects

Miss. Rahimah Bt. Othman

Email: rahimah@unimap.edu.my

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

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