Advanced Thermodynamics Note 3 Heat Effects

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# Advanced Thermodynamics Note 3 Heat Effects - PowerPoint PPT Presentation

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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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.
• 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
• 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)

constant-volume

mechanically reversible constant-volume process

.OR.

constant-pressure

mechanically reversible constant-pressure process

• 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:
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

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.

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
• 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

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

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
• 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
• 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
• 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 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:

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

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

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