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

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slide2
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.
sensible heat effects
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)
slide4

constant-volume

mechanically reversible constant-volume process

.OR.

slide5

constant-pressure

mechanically reversible constant-pressure process

slide6
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:
slide7
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

slide8

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.

slide9

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

latent heats of pure substances
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

slide11

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

slide12

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

standard heat of reaction
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:
standard heat of formation
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:
standard heat of combustion
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.
temperature dependence of h
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:
slide19

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

slide20

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

slide21

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