1. Advanced Thermodynamics Note 3 Heat Effects
Lecturer: 郭修伯

2. Heat The manufacture of ethylene glycol: Heat effects are important.
The catalytic oxidation reaction is most effective when carried out at temperatures near 250°C.
The reactants, ethylene and air are heated to this temperature before they enter the reactor.
Heat is removed from the reactor to maintain the reaction temperature at 250 °C and to minimize the production of CO2.
Heat effects are important.

3. Sensible heat effects
Heat transfer to a system in which there are no phase transition, no chemical reactions, and no changes in composition cause the temperature of the system to change.
Relation:
Quantity of heat transferred
The resulting temperature change
Two intensive properties establishes its state: U = U (T,V)

4. constant-volume
mechanically reversible constant-volume process
.OR.

5. constant-pressure
mechanically reversible constant-pressure process

6. From empirical equation:
Since or , we need C = f (T).
From empirical equation:
For gases, it is the ideal-gas heat capacity, rather than the actual heat capacity, that is used in the evaluation of such thermodynamic properties as the enthalpy.
Calculate values for a ideal-gas state wherein ideal-gas heat capacities are used
Correction to real-gas value
Ideal-gas heat capacities:
The two ideal-gas heat capacities:
The molar heat capacity of the mixture in the ideal-gas state:

7. With The function name is ICPH
Mean heat capacity; subscript “H” denotes a mean value specific to enthalpy calculations.
The function name is MCPH
It can be used to evaluate

8. Calculate the heat required to raise the temperature of 1 mol of methane from 260 to 600°C in a steady-flow process at a pressure sufficiently low that methane may be considered an ideal gas.

9. What is the final temperature when heat in the amount of 0
What is the final temperature when heat in the amount of 0.4 x 106 Btu is added to 25 (lb mol) of ammonia initially at 500 °F in a steady-flow process at 1 (atm)?
Start with a value T ≧ T0, T converges no the final value T = 1250K

10. Latent heats of pure substances
A pure substance is liquefied from the solid state of vaporized from the liquid at constant pressure, no change in temperature
The latent heat of fusion
the latent heat of vaporization
the coexistance of two phases
According to the phase rule, its intensive state is determined by just one intensive property.
Latent heat
Vapor pressure

11. Rough estimates of latent heats of vaporization for pure liquids at their normal points (Trouton‘s rule):
Riedel (1954):
Accurate! Error rarely exceed 5%
Water:
latent heat of vaporization of a pure liquid at any temperature, (Watson, 1943):
Absolute temperature of the normal boiling point
Critical temperature (bar)
Reduced temperature at Tn

12. Given that the latent heat of vaporization of water at 100°C is 2257 J/g, estimate the latent heat at 300 °C.

13. Standard heat of reaction
A standard state is a particular state of species at temperature T and at specified conditions of pressure, composition, and physical condition as e.g., gas, liquid, or solid.
Gases: the pure substance in the ideal-gas state at 1 bar.
Liquids and solids: the real pure liquid or solid at 1 bar.
All conditions for a standard state are fixed except temperature. Standard-state properties are therefore functions of temperature only.
Heat of reaction:

14. Standard heat of formation
A formation reaction is defined as a reaction which forms a single compound from its constituent elements, e.g.,:
The heat of formation is based on 1 mol of the compound formed.
The standard heat of formation : K
The standard heat at 25°C for the reaction:

15. Standard heat of combustion
A combustion reaction is defined as a reaction between an element or compound and oxygen to form specific combustion products.
Many standard heats of formation com from standard heats of combustion, measured calorimetrically.
Data are based on 1 mol of the substance burned.

16. Temperature dependence of ΔH°
A general chemical reaction:
standard heat of reaction:
if the standard-state enthalpies of all elements are arbitrary set equal to zero as the basis of calculation:
For standard reactions, products and reactants are always at the standard-state pressure of 1 bar:

18. Calculate the standard heat of the methanol-synthesis reaction at 800 °C.

19. Maximum attainable temperature → adiabatic, Q = 0 → ΔH = 0
What is the maximum temperature that can be reached by the combustion of methane with 20% excess air? Both the methane and the air enter the burner at 25°C.
Maximum attainable temperature → adiabatic, Q = 0 → ΔH = 0
Products at 1 bar and T K
1 mol CO2
2 mol H2O
0.4 mol O2
9.03 mol N2
Start with T > K and converge on a final value of T = 2066K
ΔH = 0
Reactants at 1 bar and 25°C
1 mol CH4
2.4 mol O2
9.03 mol N2

20. Catalytic reforming of CH4:
The only other reaction occurs:
Calculate the heat requirement.
Not independent, choose (1) and (3) reactions
Products at 1 bar and 1300 K
0.87 mol CO
3.13 mol H2
0.13 mol CO2
0.87 mol H2O
ΔH = 0
Reactants at 1 bar and 600K
1 mol CH4
2 mol H2O

21. 0.87 mol CH4 by (1) and 0.13 mol CH4 by (3)
Steady flow, no shaft work, kinetic and potential energy changes are negligible