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I was studying the Andrews' isotherms, virial equation of state and Van der Waals (vw) gas equation. What I understood is that Andrew did some sort of experiment to correlate the gas parameters and many people tried to find the equation governing the isotherms of Andrews. However Onne mostly, although not fully, succeeded for his virial equation but since it's only empirical and lacked physical basis, so vw gave his famous equation of state. When matched with Experimental isotherms, it goes well with some discrepancies. All resources approach this things by using the liquification of gas. Why the liquification is studied while discussing the deviation of real gas from ideal gas. Why the whole topic is revolving around the gas to liquid transition and the critical parameters? Does this mean that the old kinetic gas theory guys didn't know that gas can be liquified; that's why the Andrews' isotherms are so much important?

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Andrew's isotherms show the complete behavior of CO$_2$ from (i) ideal gas to (ii) non ideal gas to (iii) liquid. The ideal gas law describes isotherms in region (i). The virial equation with one or two coefficients describes the transition from (i) to (ii). The van der Waals equation describes fairly well all three types of behavior. A real liquid will also turn solid. This behavior is not captured by the van der Waals equation. So, the three approaches (ideal gas law, virial with few coefficicnts, and the van der Waals equation) represent increasing degree of sophistication in representing the properties of real fluids.

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