Questions tagged [equation-of-state]

Questions related to a thermodynamic equation describing the state of matter under a given set of physical conditions.

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9
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1answer
2k views

Does the van der Waals equation remain valid when repulsive intermolecular forces dominate?

The van der Waals equation for a real gas is: $$RT =\left(p+\frac{a}{V_\mathrm{m}^2}\right)(V_\mathrm{m}-b)$$ We have understood this formula by saying that $a$ is the term which is for force of ...
12
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1answer
1k views

Why do some gases have lower value of Z for a particular pressure?

In the above graph,the minima of the curve for methane is more than that of nitrogen. Also, for a given value of pressure, the value of $Z$ for methane is less than that of nitrogen. They seem to meet ...
24
votes
5answers
933 views

Why are equations of state for a non-ideal gas so elusive?

The ideal gas equation (daresay "law") is a fascinating combination of the work of dozens of scientists over a long period of time. I encountered Van der Waals interpretation for non-ideal gases ...
19
votes
2answers
3k views

What is a rigorous definition of gas volume, and how is the Van der Waals equation derived?

I am confused about the justification for the corrections to the ideal gas law in the Van der Waals equation: $$p=\frac{nRT}{V-nb}-a\left(\frac{n}{V}\right)^2$$ I understand that the equation ...
14
votes
3answers
12k views

Why is the van der Waals coefficient b equal to four times the volume of the particle?

In the van der Waals equation of state $$\left[p + a\left(\frac{n}{V}\right)^2\right](V-nb) = nRT$$ the coefficient $b$ is supposed to represent the volume occupied by the particles. Why then is it ...
6
votes
1answer
9k views

Relation between the virial coefficients and van der Waals constants

I don't know where to begin with this question. A function $f(x)$ can be expressed as a special power series called the Taylor expansion. The common expansion is $(1-x)^{-1}=1+x+x^2$ Note that the ...
2
votes
1answer
1k views

How much pressure is needed to make dry ice?

By compressing $\ce{CO2 (g)}$ the gas gains a lot of heat. When the hot compressed carbon dioxide is left to cool, it attains the temperature of the surrounding material. When it is released into the ...