Heat Effects ERT 206/4 Thermodynamics CHAPTER 4 Miss. Rahimah Bt. Othman Email: rahimah@unimap.edu.my

COURSE OUTCOME 1 CO1) Chapter 1: Introduction to Thermodynamics 2. Chapter 2: The First Law and Other Basic Concepts 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 Ethylene glycol in 3-D Chemical structure of Ethylene glycol 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. (4.1) Derive: (4.2) (4.3)

Temperature dependence of the Heat Capacity and a, b, c = constant characteristic of the particular substance Exception: ɣT2 = cT-2 (form) dimensionless CP/R = A + BT + CT2 + DT-2 or Is = 0 (4.4) Unit of Cp governed by the choice of R

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 The 2 ideal-gas heat capacity: Are related (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 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 A B C C Pmixtureig = 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 Sensible-Heat 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 conveniently expressed as; (4.7) (4.7) (4.8) (4.9) (4.10) Refer to Exp. 4.2

Use of Define Functions 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 Refer to Exp.4.3

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) (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. 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. Accurate for an impirical expression; error rarely >5% (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?

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: (4.13) (Refer to Exp. 4.4)

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 Std state of gases = ideal-gas state Degree symbols = standard state Ideal gas Std state of gases = ideal-gas state

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

Lets examine the values for several forms of oxygen. Molecular (diatomic) oxygen is the standard elemental form. Oxygen atoms (O) and ozone (O3) are higher energy forms as evidenced by the enthalpy of formation data in the table. The standard enthalpy of formation of any element in its most stable form is defined as zero. In terms of sign convention, negative numbers are used for exothermic reactions and positive numbers for endothermic reactions.

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 (4.14)

Hoi = ∆Hof if standard-state enthalpies of all elements are arbitrarily =0 Eq. 4.14 becomes: (4.15) (4.16) (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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