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Heat transfer is common in chemical industry. Combustion, extraction, distillation etc. involve heat effects that accompany physical and chemical changes with the principle of thermodynamics.
Chapter 4: Heat Effects
Source: Equations and examples adopted from Smith, J.M., Van Ness, H.C. and Abbott, M.M. Introduction to Chemical Engineering Thermodynamics, 7th Edition, McGraw-Hill, 2005(if not specified elsewhere)
Sensible heat effects (temperature change) Latent heat effects (phase transition) Heat effects of chemical reaction, formation, and combustion under standard conditions as well as actual industrial conditions Heat effects of mixing processes (not treated in this chapter)
To apply thermodynamics to the evaluation of the heat effects that accompany physical and chemical operations
Objective
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T1
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Q = ∆H = ∫ C P dT
T2
Sensible heat effects are characterised by temperature changes in a system in which there are no phase transitions, no chemical reactions, and no changes in composition.
For mechanically reversible, constant-pressure, closed-system processes / steady-flow heat transfer where ∆EP , ∆EK ≈ 0, Ws = 0
T1
Q = ∆U = ∫ CV dT
T2
Relations between quantity of heat transferred and resulting temperature change
For mechanically reversible, constant-volume, closed-system processes
Sensible Heat Effects
2.
1.
Calculation for hypothetical ideal-gas-state values Correction to real-gas values
More convenient for thermodynamic-property evaluation in two steps:
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Ideal-gas heat capacity, C Pig rather than actual heat capacity
Parameters in equation for CP can be found in App. C.
CP 2 −2 = A + BT + CT + DT R
ig
Heat Capacity:Temperature Dependence
CVig C Pig = −1 R R
Relations between the two ideal-gas heat capacities
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∑ y i C Pigi
In an ideal-gas mixture, the molecules have no influence on one another, and each gas exists independent of the others.
C Pigmix =
C Pigmix = y A C PigA + y B C PigB + y C C PigC + ...
Heat Capacity: Gas Mixtures
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T
Read textbook, Smith et al. (2005) p.130 and Ex. 4.2 for details.
To calculate Q or ∆H given T0 and T:
T
C Q = ∆H = ∫ C P dT = R ∫ dT T0 T0 R
ig P
Heat Capacity: Evaluation of the Integral
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H
(T − T0 )
∆H T= + T0 CP H
∆H = C P
(4.10)
Read textbook, Smith et al. (2005) p.130 for details.
2. Substitute H into Eq. (4.10) to get new T
1. Guess T, then calculate τ, then substitute into Eq. (4.8)
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3. Substitute new T into Eq. (4.8) to reevaluate H until iteration converges.
To calculate T given T0 and Q or ∆H (an iteration scheme is helpful):
Heat Capacity: Evaluation of the Integral
For steady flow through a heat exchanger at approximately atmospheric pressure, what is the final temperature, (a) when heat in the amount of 800 kJ is added to 10 mol of ethylene initially at 200°C (473.15 K)?
Exercise: Problem 4.2 (a)
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103 B = 14.394 B = 14.394 x 10-3 10
(
)
= 9.346
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14.394 ×10 −3 − 4.392 ×10 −6 (473.15)(2 + 1) + (473.15)2 22 + 2 + 1 + 0 = 1.424 + 2 3
∆H T= + T0 CP H
H
R CP
R
H
CP
Guess T = 400°C (673.15 K), thus τ = 2.
Exercise: Problem 4.2 (a) (cont’d)
Trouton’s rule (rough estimates at Tn) ∆H n ≈ 10 RTn
dP sat ∆H = T∆V dT
Phase transition, coexistence of two phases, no temperature change Clapeyron equation (derived in Chapter 6)
Latent Heats of Pure Substances
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P (bar)
∆H 2 1 − Tr2 = ∆H1 1 − Tr1
0.38
Watson equation (with a known value, experimental or estimated by Riedel equation)
∆H n 1.092(ln Pc − 1.013) = RTn 0.930 − Trn
Riedel equation (high accuracy, error < 5%)
Latent Heats of Pure Substances
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Positive (+) for products Negative (–) for reactants
i
∆H o ≡ ∑ vi ∆H ofi
Revision: Read Chapter 4 (4.3-4.5), Smith et al. (2005)
Standard states: pure substance at ideal-gas state at 1 bar, real pure liquid or solid at 14 1 bar
Standard Heats: Reaction, Formation, Combustion
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temperature change
chemical reaction
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temperature change
Standard Heats:Temperature Dependence
Standard Heats:Temperature Dependence
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Standard Heats:Temperature Dependence
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CO(g) + 2H2(g) CH3OH(g)
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Calculate standard heat of methanol-synthesis reaction at 800°C (1073.15 K):
Example 4.6: Standard heat at temperature other than 298.15 K
∑ν i
Ai = ∆A
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non standard-state conditions non stoichiometric proportions reaction not go to completion variation in temperature presence of inert several reactions simultaneously
Industrial reactions are often carried out under/with
Heat Effects of Industrial Reactions
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standard conditions actual industrial conditions
Sensible heat effects (as a result of temperature change) Latent heat effects (due to phase transition) Heat effects of chemical reaction, formation, and combustion under
Read Chapter 4 (Smith et al. 2005) Attempt Tutorial 3: Problems 4.11, 4.38, 4.49,4.51
Self study
In this chapter, we have evaluated the heat effects that accompany physical and chemical operations from the point of thermodynamics. We have examined
Conclusions
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