Talk:Equation of state: Difference between revisions

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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 T_c and P_c as the criticial temperature and pressure, respectively. Fine, so far.

But what is V_c? 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 V_c defined in relation to one mole of a given substance?

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

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. V_c 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 = ∑ ∑ y_iy_j(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).

@@ Line 1: / Line 1: @@
-OK, so I take the subscript "c" to refer to the [[critical properties]] which I take to be the value of those properties at
+OK, so I take the subscript "c" to refer to the [[:critical properties|critical properties]] which I take to be the value of those properties at
+the critical point (ie, the set of conditions in which [[:solid|solid]], [[:liquid|liquid]], and [[:gas|gas]] are in equilibrium.)
+So, I recognize T<sub>c</sub> and P<sub>c</sub> as the criticial temperature and pressure, respectively. Fine, so far.
-the critical point ¥ie, the set of conditions in which [[solid]], [[liquid]], and [[gas]] are in equilibrium©¤
+But what is V<sub>c</sub>? 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 V<sub>c</sub> defined in relation to one [[:mole|mole]] of a given substance?
+--JoeAnderson (never did well in p-chem)
-So, I recognize T<sub>c</sub> and P<sub>c</sub> as the criticial temperature and pressure, respectively©  Fine, so far©
-But what is  V<sub>c</sub>?  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 V<sub>c</sub> defined in relation to one [[mole]] of a given substance?
---JoeAnderson ¥never did well in p-chem¤
 ----
+Actually, the point at which the [[:solid|solid]], [[:liquid|liquid]], and [[:gas|gas]] are in equilibrium is called the [[:triple point|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. V<sub>c</sub> is the critical molar volume (ie. the volume of one [[:mole|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.
-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©  V<sub>c</sub> 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:
+a&alpha; = &sum; &sum; y<sub>i</sub>y<sub>j</sub>(a&alpha;)<sub>ij</sub>
-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:
-a&alpha; = &sum; &sum; y<sub>i</sub>y<sub>j</sub>¥a&alpha;¤<sub>ij</sub>
-If anyone knows how to do the summation signs, let me know and I'll updata the page accordingly©
+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 "a&alpha;" is not what you mean to write here. See [[:Wiki special characters|Wiki special characters]]. --[[:Lee Daniel Crocker|LDC]]
-You're forgetting the semicolons on your HTML entity references©  Also, I'm sure that "a&alpha;" is not what you mean to write here©  See [[Wiki special characters]]©  --[[Lee Daniel Crocker|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. --[[:JoeAnderson|dja]]
-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©  --[[JoeAnderson|dja]]
 ----
+LDC, thanks for the information. As for "a&alpha;", it is supposed to be "a" multiplied by the greek letter "alpha". How would you recommend it be specified?
-LDC, thanks for the information©  As for "a&alpha;", 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).