How was the van der Waals equation derived?

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1. Jun 22, 2015

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 Pmeasured+a(n/V)^2=Pideal

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 Videal-nb=Vreal

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

Is there a reason for this?

2. Jun 23, 2015

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?

3. Jun 26, 2015

sgstudent

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 PidealVreal=nRT which seems weird to me. Shouldn't both terms represent the ideal volume?

4. Jun 26, 2015

Simon Bridge

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

5. Jun 27, 2015

sgstudent

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 (Preal+a(n/V)^2)Videal=PidealVideal=nRT?