SOAVE modification of Redlich-Kwong EQUAION:
Where ω is the acentric factor for the species.
for hydrogen:
where A and B are positive.
The equation of state created by Peng and Robinson has been found to be useful for both liquids
and real gasses.
p =
R T
a ( T )
--------------------------------Vm - b
Vm ( Vm + b ) + b ( Vm - b )
p = pressure
a = empirical constant
Vm = molar volume
R = ideal gas constant
b = empirical constant
T = temperature
Thermodynamics -Chapter IV-1
Heat operations are of great importance to chemical engineers .so heat
transfer is a common operation in the chemical industry .
Heat effects are divided into in to two classes ,the first is characterized
by temperature change and is named sensible heat effects ,the other is
not accompanied by a temperature change and is named hidden or
latent heats and is characteristic of heat effects of chemical reaction,
phase transition, formation and separation of solutions.
In this chapter we will apply thermodynamics to evaluate these effects
accompanying most of the chemical and physical processes .
Sensible heat effects: heat transfer to a system in which there are no
phase transitions ,no chemical reactions and no changes in composition
Causes the temperature of the system to change.
We are to lay down the relations between the quantity of heat
transferred and the resulting increase in temperature.
For a homogeneous substance of constant composition
The transferred heat can be expressed as function of two intensive
properties ,molar Volume and Temperature and is equal to :
And thus:
Also for pressure and Temperature , H=f(P,T)
Defined functions:
ICPH denotes ideal gas specific heat based on Enthalpy calculations.
MCPH denotes mean specific heats based on enthalpy calculations.
Both functions are evaluated through a computer routines.
Latent heats of vaporization or condensation :
THESE heats are not accompanied by temperature increase or decrease
,And are estimated by the equation of CLAPEYRON :
ΔH=T ΔVdpsat/dT
The latent heat is estimated by many PROCEDURES .
The procedures known as UNIVAP can predict :
1- The heat of vaporization at normal boiling point at a pressure of 1
atm.(101325pa.)
2- Estimation of the latent heat of vaporization at any other
temperature from a known ΔH of vaporization at a known
temperature ,for pure liquids the Trouton’s rule leads to :
ΔHn/RTn=≈10 ,where Tn is the normal boiling point.
Also the riedel ‘s equation :
ΔH/RTn=1.092(lnPc-1.013)/(0.930-Trn),
this equation is accurate and errors do not exceed 5% .
Watson proposed the following equation which is accepted
widely:
ΔH2/ΔH1 ={(1-Tr2)/(1-Tr1)}0.38
Example:
Given that the latent heat of vaporization of water at 100˚C is
2257J.g-1.Estimate the latent heat at 300˚C?
Standard Heat of reaction:
For the reaction :aA+bB→lL+mM
The standard heat of reaction is defined as the enthalpy change
when a moles of A and b moles of B (in their standard states at
temperature T ) react o form l moles of L and m moles of M in
their standard states at the same T.
Standard states are assigned as :
Pure substance ,ideal gas at 1 bar for gases . and
Real pure liquid or solid at 1 bar for liquids and solids.
Property values at their standard states are denoted by the
degree symbol ˚, as Cp˚ is the standard-state heat capacity .
From the definition ,Cp˚ is the same as Cpi g as shown in appendix ,
table C-1, .
The symbol ΔH˚298 indicates that the heat of reaction is the value for a Temperature of 298.15 K.
STANDARD HEATS OF FORMATION of the reactants and products
ARE used for the estimation of the standard heat of reaction .
A FORMATION REACTION is a reaction which forms a single
compound from its constituent elements .
As in C+0.5O2+2H2→CH3OH ,THIS REACTION IS A FORMATION
REACTION ,WHERE METHANOL IS FORMED FROM ITS
constituents carbon,oxygen and hydrogen .
The standard heat of reaction is calculated as:
ΔH˚f298.15 of H2O +ΔH˚f298.15 of CO –{ΔH˚f298.15 of CO2+ΔH˚f298.15 of
H2},from table C-1 we get
-241818 J-110525 J –{-393509 J+0} =41166 J.
In the standard heats of formation we must be aware of the
phase in which the component is produced ,in the gas or in the
liquid phase . This is clearly seen in the multiple reaction of the
Water gas shift reaction to produce H2 and carbon dioxide :
ΔH˚f298.15 of H2O(g) is -241818 J and ΔH˚f298.15 of HCL (g) is -92307 J
and that of CL2 is zero ,then
the standard heat of reaction is = 0 –2* (241818) -4*(-92307)
=-114408 J.
The standard heat of combustion :
The enthalpy of the combustion reaction Is calculated as the
standard heat of reaction ,from the standard heats of formation .
see appendix C-1.
For the combustion reaction of Butane ,
C4H10 (g)+6.5O2 → 4CO2+5H2O(g)
ΔH˚r C =5(-285830)+4(-393509)-{0+(-125790)=-2877396 J/mole of
butane.
The temperature dependence of the heat of the reaction :
The standard heat is referred to standard state ( pure ideal gas at
1 bar for gases and pure liquids and solids at 1 bar) and and at T.
The Temperature on which table C-1 is based is 298.15 K.
But for any other temperature ,the heat of the reaction is to be
calculated for that temperature.
As ΔH˚T (the heat of reaction at T)=ΔH˚298.15 +∫Δcp˚dT,T(298.15 ,T)