Van der Waals gas is not real gas?

In summary, the discussion is about the van der Waals equation and its application to real gases. It is noted that at critical temperature, the first and second derivatives of pressure with respect to volume are both zero. The critical pressure and volume can be calculated using equations 1 and 2, and the critical temperature can be calculated using equation 3. However, when applying these equations to a real gas, there may be discrepancies due to the gas not perfectly obeying the van der Waals equation. This raises the question of what is meant by a "perfect" van der Waals gas.
  • #1
Outrageous
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From van der Waals , (P+a/v^2)(v-b)=RT,
At critical temperature, I get (∂P/∂V)at constant temperature =0
and (∂^2P/∂V^2) at constant temperature ,T=0.
then critical pressure,P = a/(27b^2)--------1
critical volume,v=3b-----------2
critical temperature=8a/(27Rb)----------3
then simultaneous equation 1 and 3,
I get b=(RT/8P), b=(v/3) ------------------4
But from the experiment, we get T,P,v and then substitute into the two equation from 4,both b have different values. Why?

Thank you
 
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  • #2
(P+a/v^2)(v-b)=RT

Using your equations:
P = a/(27b^2)
v=3b
T=8a/(27Rb)

I get
(a/(27b^2)+a/(9b^2))(2b)=8Ra/(27Rb)
8/(27b) = 8/(27b)

Looks fine.

But from the experiment, we get T,P,v
Are you sure your real gas is a perfect van-der-Waals gas?
 
  • #3
mfb said:
(P+a/v^2)(v-b)=RT

Are you sure your real gas is a perfect van-der-Waals gas?

I though all real gas is van der Waals ? Then what do you mean by perfect van der Waals?
 
  • #4
On other threads which you've started, it's been made clear (I think) that the V der W equation is a theoretical equation based on some quite crude assumptions. No actual gas obeys the V der W equation perfectly. [The confusion may be caused because 'real gas' is sometimes used to mean non-ideal gas, even a theoretical non-ideal gas, and not necessarily an actual gas.]
 
  • #5
for your question. Van der Waals gas is a theoretical model that describes the behavior of real gases, taking into account the size and attractive forces between gas molecules. While it is a useful approximation for many gases, it is not a completely accurate representation of real gases. Therefore, it is not surprising that there may be discrepancies between the predicted values from the van der Waals equation and experimental results.

The equations you have provided are derived from the van der Waals equation and are only valid at the critical point, where the gas undergoes a phase transition from gas to liquid. At this point, the gas properties are no longer described by the van der Waals equation and may deviate from the predicted values.

Additionally, the van der Waals equation assumes that gas molecules have a finite size and experience attractive forces, which can vary depending on the specific gas. Therefore, the values of the parameters a and b may differ for different gases, resulting in different values for b in equations 4.

In summary, while the van der Waals equation is a useful approximation for describing the behavior of real gases, it is not a perfect representation and may not always accurately predict experimental results. Other factors such as the specific properties of the gas being studied and the conditions of the experiment can also contribute to discrepancies between predicted and observed values.
 

1. What is a Van der Waals gas?

A Van der Waals gas is a hypothetical gas that takes into account the intermolecular forces between gas particles. It is named after Dutch scientist Johannes Diderik van der Waals, who first proposed this concept.

2. How is a Van der Waals gas different from a real gas?

A real gas is one that follows the ideal gas law, which assumes that gas particles have no volume and do not interact with each other. However, a Van der Waals gas takes into account the volume of gas particles and their interactions, resulting in a deviation from the ideal gas law.

3. Why is Van der Waals gas considered a model and not a real gas?

A Van der Waals gas is considered a model because it simplifies the behavior of real gases by taking into account only two factors: the volume of gas particles and their interactions. In reality, there are many other factors that can affect the behavior of gases.

4. Can Van der Waals gas be observed in real life?

No, Van der Waals gas is a theoretical concept and cannot be observed in real life. However, it is a useful model for understanding the behavior of real gases.

5. What are some examples of real gases that behave like Van der Waals gas?

Some examples of real gases that behave similarly to Van der Waals gas include carbon dioxide, ammonia, and water vapor. These gases have relatively large molecules and experience significant intermolecular forces, causing them to deviate from the ideal gas law.

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