# Talk:Equation of state

## '03 thru '05 talk

Hi How can I find Boils tempurates according to Radling - Coene equation

Hello, I was looking for the binary interaction parameters of Hydrogen and Helium for a mixture density calculation for the peng robinson E.O.S. Does any one know it or know where to find this number required for the mixing rule of the Peng? Adam R. Baxter email me at: baxter.56@osu.edu Thanks

OK, so I take the subscript "c" to refer to the critical properties which I take to be the value of those properties at the critical point (ie, the set of conditions in which solid, liquid, and gas are in equilibrium.)

So, I recognize Tc and Pc as the criticial temperature and pressure, respectively. Fine, so far.

But what is Vc? Volume, I would guess, but T and P are intrinsic properties of the system, whereas volume is extensive, ie, it depends on "how much" material there is. Is Vc defined in relation to one mole of a given substance?

--JoeAnderson (never did well in p-chem)

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Actually, the point at which the solid, liquid, and gas are in equilibrium is called the triple point. The critical temperature is that temperature above which unique liquid and gas phases do not exist. As you approach the critical point, the properties of the gas and liquid phase become the same, so above the critical temperature there is only one phase. The critical pressure refers to the vapor pressure at the critical temperature. Vc is the critical molar volume (ie. the volume of one mole) and as such is more like a density (or 1/density) than an actual volume. Note that in all of the listed equations of state, V is defined as the molar volume. This is why PV = RT, instead of PV = nRT.

--Matt Stoker

In order to be more complete, we really should add mixing rules for each equation of state (ie. rules for determining the correct parameters for a mixture). In order to add these we need a summation sign. For example for the Soave Equation, the rules are:

aα = ∑ ∑ yiyj(aα)ij

If anyone knows how to do the summation signs, let me know and I'll updata the page accordingly.

--Matt Stoker

You're forgetting the semicolons on your HTML entity references. Also, I'm sure that "aα" is not what you mean to write here. See Wiki special characters. --LDC

Thanks, Matt! Your discussion above of triple point, critical temperature, critical molar volume, etc. makes it all much more clear, I think. I'd like to see that worked into the main page--if you'd like to do it, that would be fine. I'll wait a while to give you a chance at it, or will go ahead and do it at some later point. --dja

LDC, thanks for the information. As for "aα", it is supposed to be "a" multiplied by the greek letter "alpha". How would you recommend it be specified?

-- Matt Stoker

Hello, this page had a lot of garbage characters introduced into it somehow (periods became copyright symbols; parentheses became yen). I just pasted in an earlier version of this page from Equations of State (2 caps). I've looked it over and it seems to be ok; please double-check (I'm not a scientist).

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Hi guys

How do I modify the page to add a new equation of state? I don't understand the editing system well enough to add a new item to the list.

cheers

Robinh 20:41, 10 Dec 2003 (UTC)

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I think this article should merely refer to the various articles describing the different equations of state: Ideal gas law, Van der Waals equation and so on, instead of repeating them. Bo Jacoby 11:35, 13 October 2005 (UTC)

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I totally agree, why repeat what is already there. This page should be used to describe when and how the equations are used with respect to each other. Do you have any thoughts to what the specific layout should be for the new page? Thales

In order to add the mixing rules for the equations of state, it will be necessary to add an entire page on it, as several sets of mixing rules are available (see the reference Valderrama for a discussion).

--Ascentury 03:55, 1 May 2007 (UTC)

## State functions?

Are equations of state related to State functions? - ElAmericano | talk 21:28, 29 January 2006 (UTC)

Yes. Pressure, volume and temperature are state functions, and the equation of state relates them. The equation of state is not sufficient, however. Some other equations must tell the entropy and the energy of the state. Bo Jacoby 09:55, 31 January 2006 (UTC)

## Isn't pressure written with a small P?

As in the:

=== Classical ideal gas law ===
$PV=nRT\,$ Shouldnt it be:

$pV=nRT\,$ ? — Preceding unsigned comment added by 81.228.244.89 (talk) 15:15, 14 November 2006, (UTC)

Agree, the general usage is assign lowercase letter for intensive variables and uppercase for extensive variables. For example:
$V$ for volume (Units: $m^{3}$ ) and $v$ for specific volume (Units: $m^{3}/kg$ ),
$H$ for enthalpy (Units: $J$ ) and $h$ for specific enthalpy (Units: $J/kg$ or $J/mol$ ).
$T$ for temperature is an exception for present usage (in old texts they refer to temperature by $\theta$ instead of $T$ ). -- Myth (Talk) 10:59, 6 March 2007 (UTC)

A standard reference: IUPAC pressure notation — DIV (128.250.80.15 (talk) 07:18, 12 September 2008 (UTC))

## SAFT equation

Hi do you think that there should be something on this page about the SAFT equation of state, given that its now one of the most modern approaches for this area? — Preceding unsigned comment added by 129.31.67.66 (talk) 10:04, 3 December 2006 (UTC)

The introduction mentions:

In physics and thermodynamics, an equation of state is a relation between state variables.

But the article only deals with state relationship between pressure, temperature and volume. It does not describe any other state equations like:

$H=C_{p}T$ or $dH=TdS-pdV$ I think the title of the article is misleading. Either the title should be changed to something more appropriate or the text should also cover other equation of states. The former is a better option given the size of the article. -- Myth (Talk) 10:59, 6 March 2007 (UTC)

## Ideal gas law and Euler equations

I have deleted the following statement which refers to the ideal gas law in the form$P=\rho \left(\gamma -1\right)e$ .

"This form is purely in terms of intensive quantities and is useful when simulating the Euler equations because it expresses the relationship between internal energy and other forms of energy (such as kinetic), thus allowing simulations to obey the First Law."

The equation of state ("this form") does not express the relationship between internal energy (e) and kinetic energy (for example) (there is no specific kinetic energy term $v^{2}/2$ in the equation of state?) Making Euler simulations (I assume this refers to computational fluid dynamics, CFD) obey the first law is independent of how you express the gas law. To keep the idea you would have to add something like $e=e_{total}-v^{2}/2$ where $e_{total}$ is the total intrinsic (specific) energy of an element of fluid moving with speed $v$ . E4mmacro 23:43, 10 April 2007 (UTC)

## Virial Equation of State

In the book we are using for Physical Chem class (Thermodynamics, Statistical Thermodynamics, & Kinetics by Thomas Engel and Philip Reid. ISBN 0-8053-3844-6) it states on page 151 that the virial equation is only valid over it's convergence range, which is only under relatively low pressures (Vm > 1 ??). If anyone can confirm this, it should probably be mentioned in the article. I did some calculations using values smaller than 1 and got unreasonable results. Aurimas 20:27, 6 September 2007 (UTC)

The virial equation of state can be used at higher densities (and pressures) so long as the series is convergent and enough coefficients are used. You should have low expectations of the series converging unless you're in the gas phase, so it's best to stay out of temperatures / densities where the gas phase isn't stable. Ajschult (talk) 03:18, 11 June 2008 (UTC)

How does the Virial equation relate to Virial stress? 72.74.211.41 02:00, 17 October 2007 (UTC)

The equations $B=-V_{c}\,$ and $C={\frac {V_{c}^{2}}{3}}$ need much more context or should be deleted entirely. The given values for B and C are approximations that are reasonable at the critical temperature. They can be derived by assuming that higher order coefficients (D and above) are 0 and that the critical Compressibility factor is 1/3 (which is reasonable for most fluids). The given values should certainly not be used away from the critical temperature (so the equations as stated are simply wrong). In general, the result doesn't seem sufficiently useful to warrant existing on the page.

In the current state, the first subsection of [Equation_of_state#Virial_equations_of_state] ends with an incomplete sentence, please correct that as soon as possible if you know how it should end. --Rubik's Cube (talk) 09:44, 9 July 2008 (UTC)

## Beattie-Bridgeman equation of state

The book mentioned in the above section (Thermodynamics, Statistical Thermodynamics, & Kinetics by Thomas Engel and Philip Reid. ISBN 0-8053-3844-6) also lists another "widely used" equation of state - the Beattie-Bridgeman equation of state. It uses 5 experimentally determined parameters:
$P={\frac {RT}{V_{m}^{2}}}\left(1-{\frac {c}{V_{m}T^{3}}}\right)(V_{m}+B)-{\frac {A}{V_{m}^{2}}}$ where
$A=A_{0}\left(1-{\frac {a}{V_{m}}}\right)$ and   $B=B_{0}\left(1-{\frac {b}{V_{m}}}\right)$ I am not sure what A0 and B0 stand for. If anyone knows and this formula is not yet on the page (I couldn't find it), please add it. Aurimas 20:44, 10 September 2007 (UTC)

## Nomenclature

While the standard symbol for pressure, p, is now used in the text (cf. above), the usage of subscripts still needs to be amended. See IUPAC (Mills & Metanomski, 1999).
—DIV (128.250.80.15 (talk) 07:22, 12 September 2008 (UTC))

The abbreviation EOS is never properly introduced and neither is it written bold EOS. -- Arnero (talk) 12:55, 20 December 2009 (UTC)

## E = M C^2 as equation of state

Taking into considerations E = M C^2, different type of matters with respect of their density's, differently reflects, i.e. in a different patterns, the Vacuum energy fluctuations (Casimir effect). In my opinion, the synchronized reflections of vacuum energy fluctuations off of a mass constitute the gravitational forces for that mass. In compression to a lesser density mass such as the earth, the matter in the black hole within the event horizon (equation of state), (UC Berkeley, September 24, 2010, high pressure experiments reproduce mineral structure 1,800 miles deep in the earth: where seismic waves have different patterns when run through post-pervoskite's zone of Magnesium silicate perovskite (MgSiO3) above the earth core). In my opinion, The Matter of a lesser density such as the earth matter, would react differently than the matter of the Black Hole to Vacuum waves, vacuum fluctuations, vacuum energy, which (the vacuum energy fluctuation ) when reflected off of these two different matters (equation of state) creates different synchronized reflected vacuum energy waves i.e. different gravitational forces; Where synchronized reflected vacuum energy waves is a gravitational force for a set, a defined system that has a specific equation of state. Also, The matter of the Black Hole (within the event horizon) may not reflects electromagnetic waves, since light have two components vectors: electric and magnetic, as it (the light) does reflects off of a lesser denser mass's such as the earth; therefore no light reflects off of a black hole matter, as observed. (UC Berkeley, September 24, 2010, high pressure experiments reproduce mineral structure 1,800 miles deep in the earth: where seismic waves have different patterns when run through post-pervoskite's zone of Magnesium silicate perovskite (MgSiO3) above the earth core). Or/and, the vacuum, vacuum energy of the atmosphere of a black hole will not support to carry light waves (or, most electromagnitic waves within the "atomspher" of the mass of the black hole. and light speedThat constitute that If we defined the atmosphere of a black hole to be the space between it's event horizon and it's mass surface, and if the rules of equation of state where to apply within the event horizon of a black hole atmosphere's with consideration to light travel; then E = M C^2 as an equation of state, could not probably be applied or used within the atmosphere of a black hole. E = M C^2 is does not apply in the black hole as a Equation of state for the absence of most electromagnetic waves spectrum (Hawking radiation existence?).--e:Y,?:G 19:58, 25 September 2010 (UTC)--e:Y,?:G 19:58, 25 September 2010 (UTC) —Preceding unsigned comment added by E:Y,?:G (talkcontribs)

In the discussion where it says "For Pr<1 and Tr<1, the system is in a state of vapor-liquid equilibrium. The reduced cubic equation of state yields in that case 3 solutions." This is not strictly true. It would be better to say that the system will have a finite range of p over which it has 3 solutions. There are certainly values of Pr and Tr both less than 1 which do not yeild 3 solutions. Luriol (talk) 22:32, 22 November 2010 (UTC)

## Factor a in Van der Waals equation of state off by a factor of 0.1?

Hello

So I have a lab exam in Joule-Thomson effect and I have given values for a and b for VdW equation of state for nitrogen and carbon dioxide. When I take the critical temp. and pressure and put the equation on this site, b gives correct value, but a is off by a factor of 0.1.

E.g. For $CO_{2}$ , given in the table (the experiments and the Phywe can't be wrong) $a=3.60Pa\ m^{6}\ mol^{-2}$ , and if I put the values from the critical point page, I get: $a=3.60\times 10^{-1}\ Pa\ m^{6}\ mol^{-2}$ . Not only for carbon dioxide, but for nitrogen too...

What is even weirder is that b is correct for the same temps and pressure.

So can someone find where this comes from? I calculated from Zemansky and Dittman the coefficients a and b and they are fine. —Preceding unsigned comment added by 89.164.52.165 (talk) 19:06, 16 March 2011 (UTC)

## Cosmology obsession

There seems to be an obsession throughout the article with the use of EOS for astrophyisic use ???? why is this ?? I find it unnecesary. — Preceding unsigned comment added by 190.97.61.108 (talk) 19:11, 15 September 2011 (UTC)

## predicting...

The overview article sounds like the EOS is a cookbook in alchemistry. The EOS does not predict anything but is a model (summary, extrapolation, fit) of state variables which otherwise would be only accessible by severe quantum mechanical many-body calculations. R. J. Mathar (talk) —Preceding undated comment added 18:54, 24 February 2012 (UTC).