Ideal gas equation:
Comparison of Equations of State for Gaseous CO2
Comparison of Equations of State for Gaseous
CO
2
This exploration compares common equations of state with experimental data for gaseous . The ideal gas model is a rather harsh approximation and assumes that particles don’t interact with each other and that gas particles are essentially point particles with no volume. The van der Waals equation of state corrects for nonzero volume and also includes a pressure correction that allows for inter-particle attraction. The attraction would cause the measured pressure to be lower than that predicted by the ideal gas equation of state. The Redlich–Kwong equation of state is an empirical equation that fits experimental measurements above the critical temperature quite well. The model equations are provided here, and all symbols have their standard meaning.
CO
2
June 23, 2017—Arun Sharma
P=nRT
V
m
(
1
)van der Waals equation:
P+(-b)=RT
a
2
V
m
V
m
(
2
)Redlich–Kwong equation:
P=-b-(+b)√T
RT
V
m
a
V
m
V
m
(
3
)Functions for Calculation
Functions for Calculation
We have analyzed experimental data for at three different temperatures: 293 K, 323 K and 373 K. The critical temperature of is 304.25 K.
CO
2
CO
2
Ideal gas equation of state: The model assumes that gas particles are point particles and do not interact with each other. The function calculates the pressure according to the ideal gas model. rgas is the universal gas constant:
In[]:=
rgas=Quantity0.08206,;idealgasP[t_,v_]:=
"Liters""Atmospheres"
"Moles""Kelvins"
rgast
v
van der Waals equation of state: This model assigns a nonzero volume (parameter b) for particles and also includes attractive interaction (parameter a) between gas particles:
In[]:=
vdwgasP[t_,v_,a_,b_]:=-aCO2=Quantity3.952,"Atmospheres";bCO2=Quantity0.042,;
rgast
v-b
a
2
v
2
"Liters"
2
"Moles"
"Liters"
"Moles"
Redlich–Kwong equation of state: This model also assigns nonzero volume and attractive interaction between particles. It is generally seen as a huge improvement over the van der Waals model:
In[]:=
rkgasP[t_,v_,a_,b_]:=-v(v+b)ACO2=Quantity63.752,;BCO2=Quantity0.029677,;
rgast
v-b
a
1/2
t
"Atmospheres"
2
"Liters"
1/2
"Kelvins"
2
"Moles"
"Liters"
"Moles"
293 Kelvin
293 Kelvin
323 K
323 K
373 K
373 K
Hands-on Exploration
Hands-on Exploration
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6/23/17