Van der waals & Andrews curve: discrepancy

In summary, the Pressure versus Volume isotherms of a real gas obtained from the van der Waals equation of state overlap with experimentally obtained isotherms for carbon dioxide gas, except for in the region of phase transition where Andrews' curve gives a straight line while van der Waals predicts a maxima and minima. This discrepancy can be explained by the inclusion of intermolecular forces in the van der Waals equation, which can account for metastable states that are not achievable under experimental conditions.
  • #1
samreen
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Homework Statement


the Pressure (P) versus Volume (V) isotherms of a real gas theoretically obtained form van der waals equation of state approximately overlap with the experimentally obtained isotherms of Andrews for carbon dioxide gas. However, for those isotherms below the critical isotherm,in the region of phase transition, Andrews curve gives a straight line, while van der waals gives a maxima and minima. i need a proper and substantial explanation for the discrepancy



Homework Equations


(P + a/V2)(V – b) = RT

since its a cubic eqn, either all 3 roots will be real, or only one. but i don't see how that's relevant here.

The Attempt at a Solution



the maxima and minima represent metastable states that arent realisable under experimental conditions, and were thus not obtained by Andrews
 
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  • #2
. van der waals equation of state includes intermolecular forces, which are neglected in the ideal gas law and in Andrews' equation, so it is able to account for metastable states.
 

1. What is the Van der Waals curve and Andrews curve?

The Van der Waals curve and Andrews curve are two different mathematical representations of the same phenomenon - the relationship between pressure and volume of a gas at a constant temperature. They both describe the deviation from ideal gas behavior at high pressures.

2. What is the discrepancy between the Van der Waals curve and Andrews curve?

The discrepancy between the Van der Waals curve and Andrews curve is the difference in their mathematical equations and resulting curves. While both curves show a deviation from ideal gas behavior, the Van der Waals curve has a more pronounced S-shaped curve, while the Andrews curve has a more gradual curve.

3. Why do the Van der Waals curve and Andrews curve differ?

The Van der Waals curve and Andrews curve differ because they were developed by two different scientists, Johannes Diderik van der Waals and Thomas Andrews, using different approaches and assumptions. Van der Waals used the concept of intermolecular forces to modify the ideal gas law, while Andrews used empirical data to create his curve.

4. What is the significance of the discrepancy between the Van der Waals curve and Andrews curve?

The discrepancy between the Van der Waals curve and Andrews curve highlights the limitations of the ideal gas law and the need for more complex models to accurately describe the behavior of real gases. It also shows the importance of considering intermolecular forces and empirical data in understanding gas behavior.

5. How are the Van der Waals curve and Andrews curve used in scientific research?

The Van der Waals curve and Andrews curve are used in scientific research to model and predict the behavior of real gases at high pressures. They are also used to study phase transitions and critical points of gases. Additionally, the discrepancies between the curves have led to further research and development of more accurate gas laws and equations of state.

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