# 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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### 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 ...
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### Why is the pressure correction added in the Van der Waals equation?

Since real gas particles experience attraction to each other, that means the pressure must be less from what we would expect. So why do we have to add a term to correct it? For example, in the ...
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### Why is the pressure correction in the van der Waals equation proportional to (n/V)^2?

The van der Waals equation for real gases is stated as follows: $$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$ For the coefficient $b$, we can reason out that more the number of molecules, the ...
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### What is the chemical equation, along with the change in heat of the crystallization process of Sodium Acetate

This is the reaction found in chemical hand warmers, and I can't figure out the equation and the change in heat. Any help would be greatly appreciated
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### 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 ...
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### Calculating phase diagram of mixed component natural gases (Bubble and Dew points)

I'm developing a piece of software which calculates and plots the Phase diagram (PT) for a mixed component natural gas. For reference I have a common used natural gas plotted using a commercial ...
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### 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 ...
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### How to solve constants out of the internal energy equation?

Imagine we deal with a new kind of matter, whose state is described by: $$PV = AT^3$$ Its internal energy is given by $$U = BT^n \ln\left(\frac{V}{V_0}\right) + f(T)$$ where $A$, $B$ and $V_0$ is a ...
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### How to use a modified Peng-Robinson equation to calculate a density?

I'm trying to use the Peng-Robinson-Stryjek-Vera 2 (PRSV2) Equation of State to calculate the density of a compound, in this example: methanol. At ambient temperature and pressure, shouldn't I be able ...
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### What is the relation between universal gas constant R and amount of substance n?

I have found it mentioned in various sources that the value of R depends on the amount of substance $n$ in the ideal gas equation: $PV=nRT$ If this is true, it would imply that $R$ is a function of $n$...
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### Using Mathematica to Plot an Isotherm at its Critical Temperature

Hello I'm new to mathematica and I have been trying to plot an isotherm for a substance at its critical temperature, using Van der Waals equation of state. I have done all the work except I do not ...
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 ...