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# 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 can't equations of state be replaced by machine learning models?

The Peng-Robinson equation of state, for example, has no underlying physical meaning, and is just a model that was fit to data. Computer scientists have developed much, much better models for data ...
982 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 ...
49 views

### 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 ...
111 views

### Calculating dew point and bubble point of gas mixtures

How do you calculate approximately the triple point and critical point of any given CH-based gas mixture? I have developed a software which uses iterations to find bubble point and dew point of any ...
11k 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 ...
294 views

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 $A$, ... 0answers 6k views ### dU/dV in van der Waals equation of state derivation Previous, I proved that $$\frac{T_2}{T_1}^{C_V/(C_p-C_V)}=\frac{V_1}{V_2}$$ I've been asked to derive a similar expression for a gas that obeys the equation of state $$p=\frac{RT}{(\overline{V}-b)}... 1answer 57 views ### Simple alternative to UNIFAC to prove that a mixture containing 1ml of x and 5 litres of propylene glycol is not flammable? Section 2.6.1 of the REGULATION (EC) No 1272/2008 (CLP) defines a flammable liquid as: Flammable liquid means a liquid having a flash point of not more than 60 ^{\circ}C. So data on flash ... 1answer 88 views ### Reaction energy of oxygen and hydrogen From the bonding energy of following bonds that I found in a Wikipedia article, I calculated the reaction energy that would be released when oxygen and hydrogen are reacted to produce water. The phase ... 2answers 12k views ### Why is the pressure correction in the van der Waals equation proportional to (n/V)^2? The van der Waals equation for real gases is stated as follows:$$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRTFor the coefficient b, we can reason out that more the number of molecules, the ... 1answer 139 views ### Why is excluded volume in van der Waals equation divided by 2? Source: Physics Stack Exchange The excluded volume calculated based on the diagram is 8 times the volume of a molecule. The volume is then divided by 2 to give the so-called excluded volume per ... 0answers 60 views ### Calculating the number of energy states in a particular momentum direction Given is a 2D scenario of a particle within a container: The circumference shows all the possible 2D spatial directions for a given momentum value of the particle. One of those momentum directions is ... 2answers 91 views ### Intuituve reason for the constant of proportionality 2/3 in pv=nRT=(2/3)U Why is there a \frac23 term? I fully understand that it makes sense for pressure to be the volume weighted average kinetic energy. And the equation above shows that this is so (for an ideal gas). I ... 3answers 30k views ### Why does small value of van der Waals gas constant “b” ensure easier liquefication? Larger value of b signifies that the size of the molecules is larger and hence the forces acting should become larger due to increased surface area.This should ensure easier liquefication. But my book ... 1answer 307 views ### Why is the pressure correction constant 'a' independent of temperature? In the van der Waals equation of state, 'a' which is the correction value is based on inter-molecular forces of attraction? Then should inter-molecular forces decrease when temperature increases, and ... 1answer 55 views ### How to determine if pressure surpasses capacity with the van der Waals equation of state? I have to decide whether a \pu{20 L} container with \pu{0.8 kg} ethane can withstand the pressure at \pu{373.15 K}. The following information is given: \begin{align} b &= \pu{6.448x10^-2 ... 1answer 312 views ### Is this equation of state original? I created this equation of state as a personal undergraduate summer project (here is the link) seven years ago:\frac{PV}{nRT}-1 \propto \left(\frac{nRT}{PV}\right)^2 \left[\left(\frac{nRT}{PV}\... 1answer 488 views ### 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 ... 1answer 4k views ### 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 substancen$in the ideal gas equation:$PV=nRT$If this is true, it would imply that$R$is a function of$n$... 1answer 854 views ### 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 ... 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 ... 3answers 13k 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 ... 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 ... 1answer 1k views ### Why is the ideal gas law so ubiquitous? Why is the ideal gas law usable in most gas problems? For example, in a problem like this: "Suppose you have$1.00\: \mathrm{mol}$of a gas at$0\:^\circ \mathrm{C}$, occupying a container which is$...
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 ...