Advanced Thermodynamics Note 3 Heat Effects

1. Advanced ThermodynamicsNote 3Heat Effects Lecturer: 郭修伯

2. Heat • The manufacture of ethylene glycol: • 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. 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 0.4 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. Vapor pressure Latent heat

11. Absolute temperature of the normal boiling point • 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): 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 : 298.15 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. 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 > 298.15 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