The Van der Waals Constants
The constants and are different for different substances. We can get the estimates of and of a substance by knowing the critical values of that substance.
Before we proceed further, let us look at the mathematical function ![](images/image006.gif)
For the maximum value of x: and ![](images/image010.gif)
For the minimum value of x: and ![](images/image014.gif)
For the point of inflection, and ![](images/image017.gif)
From the Figure 9.2 we can see that the critical point is a point of inflection.
The critical isotherm must show a point of inflection at the critical point
![](images/image019.gif)
|
(10.1) |
![](images/image021.gif) |
(10.2) |
At the critical point, the Van der Waals equation is
![](images/image023.gif) |
(10.3) |
One can solve the above three equations to obtain
![](images/image025.gif) |
(10.4) |
Alternatively, one can calculate the Van der Waals constants and in terms of critical constants.
![](images/image027.gif) |
(10.5) |
The constants and can be determined for any substance from the critical point data (Table 10-1) At the critical point, one can see that
![](images/image029.gif) |
(10.6) |
Table 10.1 Some typical values of Van der Waals constants |
Gas |
Constants ![](images/image002.gif)
kPa (m3/ kmol)2
|
Constants ![](images/image004.gif)
( m3/ kmol ) |
Air
|
135.8 |
0.0364 |
Ammonia (NH3 )
|
423.3 |
0.0373 |
Carbon-dioxide(CO2 )
|
364.3 |
0.0427 |
Hydrogen (H2 )
|
24.7 |
0.0265 |
Oxygen (O2 )
|
136.9 |
0.0315 |
Nirtogen (N2 ) |
136.1 |
0.0385 |
![](images/image035.gif)
|