# How was the van der Waals equation derived?

• sgstudent
In summary: 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?
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?

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?

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

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

Simon Bridge said:
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 (Preal+a(n/V)^2)Videal=PidealVideal=nRT?

## 1. How did van der Waals come up with his equation?

The van der Waals equation was proposed by Dutch physicist Johannes Diderik van der Waals in 1873. He developed the equation based on his observations of the behavior of real gases and the limitations of the ideal gas law.

## 2. What are the assumptions made in the van der Waals equation?

The van der Waals equation makes two main assumptions: 1) that gas molecules have a finite volume, and 2) that there are attractive forces between gas molecules. These assumptions help to account for the deviations from ideal gas behavior.

## 3. How does the van der Waals equation differ from the ideal gas law?

The ideal gas law assumes that gas molecules have no volume and do not interact with each other. The van der Waals equation takes into account the finite volume of gas molecules and the attractive forces between them, resulting in a correction factor for pressure and a reduced molar volume.

## 4. What is the significance of the van der Waals equation in thermodynamics?

The van der Waals equation is an important tool in thermodynamics as it provides a more accurate description of the behavior of real gases compared to the ideal gas law. It is also used in the study of phase transitions and critical points.

## 5. Can the van der Waals equation be applied to all types of gases?

No, the van der Waals equation is not applicable to all types of gases. It is most accurate for gases that have relatively large molecular sizes and strong intermolecular forces, such as water vapor and carbon dioxide. It is less accurate for gases with small molecules and weak intermolecular forces, such as hydrogen and helium.

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