Advanced Thermodynamics

draweryaleMechanics

Oct 27, 2013 (3 years and 9 months ago)

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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.


Heat is removed from the reactor to maintain the
reaction temperature at 250
°
C and to minimize the
production of CO
2
.


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


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:



With







Mean heat capacity; subscript
“H” denotes a mean value
specific to enthalpy calculations.

It can be used to evaluate

The function name is ICPH

The function name is MCPH

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 10
6

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


T
0
, 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.

Latent heat

Vapor pressure


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

Reduced temperature at T
n

Critical temperature (bar)

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:

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

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

Reactants at 1 bar and 25
°
C

1 mol CH
4

2.4 mol O
2

9.03 mol N
2

Products at 1 bar and T K

1 mol CO
2

2 mol H
2
O

0.4 mol O
2

9.03 mol N
2

ΔH = 0

Start with T > 298.15 K
and converge on a final
value of T = 2066K

Catalytic reforming of CH
4
:

Reactants at 1 bar and 600K

1 mol CH
4

2 mol H
2
O

Products at 1 bar and 1300 K

0.87 mol CO

3.13 mol H
2

0.13 mol CO
2

0.87 mol H
2
O

ΔH = 0

The only other reaction occurs:

Calculate the heat requirement.

Not independent, choose
(1) and (3) reactions

0.87
mol CH
4

by (1) and 0.13 mol CH
4

by (3)

Steady flow, no shaft work, kinetic and
potential energy changes are negligible