How was the van der Waals equation derived?

[sgstudent]

the equation (P+a(n/V)^2)(V-nb)=nRT was derived in this manner:

The pressure of a real gas is affected by intermolecular forces and so the a(n/V)^2 term must be added to the measured pressure to obtain the ideal pressure where P_measured+a(n/V)^2=P_ideal

On the other hand when they explained the volume, they stated that the molecule had a finite size so we had to subtract the measured volume with the nb term to get the actual volume of the gas. So essentially V_ideal-nb=V_real

So this seems pretty weird to me.. For the P+a(n/V)^2 term we are substituting values to get P_ideal while for the V-nb term we are substituting values to get V_real

Is there a reason for this?

 

[Simon Bridge]

Yes. It is often useful to work in terms of idealized situation when you want to know the physics more qualitatively but when you do experiments you need to be able to anticipate the real-world values. So it is unclear what your objection is?

 

[sgstudent]

Yes. It is often useful to work in terms of idealized situation when you want to know the physics more qualitatively but when you do experiments you need to be able to anticipate the real-world values. So it is unclear what your objection is?

I'm not sure why the (P+a(n/V)^2) term represents the ideal pressure while the (V-nb) term represents the real volume, The equation is essentially P_idealV_real=nRT which seems weird to me. Shouldn't both terms represent the ideal volume?

 

[Simon Bridge]

Is the "real volume" not a modification of another variable called "ideal volume" already?

 

[sgstudent]

Is the "real volume" not a modification of another variable called "ideal volume" already?

Yes it is a modification of the ideal volume. Since we are trying to equate the van der Waals equation to the ideal gas equation (PV=nRT), shouldn't the V-nb in the equation just be V? So we have (P_real+a(n/V)^2)V_ideal=P_idealV_ideal=nRT?