h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Sorry... The other PR post was in a 'bad' format.

http://www.bbc.co.uk/h2g2/guide/A666812

Thermodynamics is important.

The state equation for a gas is the heart-piece of thermodynamical reasoning (at least for gases).

In this article I present the three most common state equations for gases. The ideal gas formula (which is taught in school). The 'van der Waals' equation, for advanced readers. And finally the virial equation which is the ultimate, yet a little more complicated, formula.

Comments wellcome.

HELL

Hoo boy, this takes me back... a little too far back Anyway, some comments.

The first sentence reads a bit awkwardly (as does this post...) I'd join it to the second sentence to read "The gas state equation is used to calculate certain properties of gases, namely: Temperature (T), pressure (p) and volume (V)."

Thermodynamics and Gases, Paragraph 2. Possibly better to say "heat moves slowly in these materials". Then again, heat moves fairly briskly in metals... hmmm, maybe better to drop that bit, and just mention the requirement for huge pressures to see interesting things Ah, what the heck, there are enough chemists and the like around here to sort out that point...

Ditto paragraph 3 - "adding heat", not temperature.

Equations; The trouble with using the dot notation (IMO) is that it looks a little confusing when you have decimal points in the expression as well (for instance, in the definition of Avagado's Number in Footnote 3). I'd say you have four choices here:

- Use * as the multiplication symbol. Has the advantage that every browser should display it, and is used for this purpose in spreadsheets etc.

- Use or ⋅ which claims to be the dot operator. This one doesn't work for me though (IE 5.5 running on Win 2000).

- Use or • which is a bullet (I can see this one at least). Basically these give you a larger dot, which make is a little more obvious.

- Go tell me to stick my head in a pig, certainly the least work and most amusing option (from your end, anyway).

Rather odd that I can't find a multiplication sign on the entities page, but there you go...

The 'van der Waals' Gas equation...

Nobel biscuit - like it

"The other modification is due to the particles sticking to eachother, a phenomenon called cohesion". Missing space! Also, I think the term sticking is perhaps misleading, as it makes me think that the particles are aggregating (i.e. condensation). It might be better to say that the particles attract each other (weakly, for the most part).

Paragraph 2 last line "compesated" -> compensated

Oddly enough, one of my class administrators in my degree was one of the people who do the measurements to get a and b for the reference books. It sounds possibly the most mind-numbing job known to man

Right, I'm meant to be correcting my thesis at the moment, so I'll stop there for now. I reckon this should go in no problem

Just two points:

- I'm wondering why *water* is listed there -- until now I thought of it as a liquid thing?

- If you take the series expansion (the virial equation) and remove everything following the factor B then of course it will be simpler than the v.d.Waals equation: it'll be reduced to
p(V-B) = nRT

It is only if you keep more terms in it that the equation is more complicated

Other than that: from me!


Hmm, there's another 'gas' entry around here

This is very good (no surprise from this author...) but I think another entry suggests itself...

There is in this entry, as in the mind of most people, some confusion betweent the concepts of "heat" and "temperature". A short entry is, I think necessary, making clear that "temperature" is a thermodynamic variable like volume, pressure, enthalpy or Gibbs free energy, whereas "heat" is another word for "energy", and it is the transfer of heat into and out of thermodynamic systems which affect the variables. You could then link from here to that explanation, and replace many of the occurrences of the word "temperature" with the word "heat". I'd write it myself, but I think Hell would do a better job...

Suggested title: "VAST GUPH - The Thermodynamic Variables".

Other than that - should be well in.

H.

OK, Hello everybody, thanks for your input.

Here come my justifications:

1 - Jamie:

The first sentence was intended to break the ice. Like: 'You might not notice, but you're confronted with the state equation in your mundane everyday life, everytime you listen to the weather forecast.'

Heat moves slow in solids and liquids. A lot slower than in gases, even in metals. It's right that metals conduct heat quite well, but you also have transport, convection and other funny things. I've added a footnote for clarity.

Equations and dot notation. Two problems: 1) Many people don't understand the omission of the dot like in pV = nRT - I am a tutor in thermodynamics for this semester, and one of my students asked me what pV was, only later I understood he didn't know pV is the same as p multiplied with V, he thought it was something like the pH, the negative logarithmus of the Volume... Anyways - I'd rather leave an operator in there, but the alternative 'x' is too ugly. With the scientific notation for constants like Avogadro's number it's the same - I feel there should be an operator in there. 2) without the dot the equation looks too condensed and chunky.

Nobel biscuit - good one, eh?

About the sticking... Hmmm , it's not that they just attract each other. They also repulse eachother... I think the problem is more like this: Two gas particles collide, and instead of bouncing off like a snooker ball (ideal gas) they stick together for a little while, as if the snooker ball was covered with honey or tar. When this sticking becomes stronger than the bouncing, the gas will liquefy, or condense, as you correctly noted... So I'd rather leave the 'sticking' in there, perhaps with a footnote? What do you think?

(Your poor class administrator has probably done something very ugly in his life to be punished with that...)

2 - Bossel (@ Bosselhilti)

Water is quite present as a gas in the atmosphere - ever wondered why it rains?

About the Simple B: B is not really B it's more correctly B(T), a function of the temperature, and this one can be very complicated. To make it simpler I chose not to get into details. But believe me: The virial equation is more complicated than it looks.

3 - Hoovooloo (formerly known as Impressive Trouser)

Heat and temperature parts have been adapted as you and Jamie suggested. It's really better now.

A new entry on other thermodynamical stuff is planned. But let us start from the start. Next one will be about the Kinetic gas theory.

----------------

and thank you all,

HELL

BTW: There is already an edited entry on the three laws of Thermodynamics. But it's a little poor IMO. Does anyone know what it takes to get an older edited entry replaced or improved?

HELL

A nice looking entry Hell from a quick look at it.
In the bits about the equations (especially the ideal gas equation) I'd be interested in seeing where this breaks down and starts to go wrong. From what I have read in scuba diving literature (forgetting the basic gas laws can get you killed here very easily) the ideal gas equation starts breaking down at only moderatly high pressures (300bar).

Hi, Hell!
I'll leave the comments on the entry itself to people who can do it justice.

With regard to replacing or updating edited entries, I know of three different procedures:
- Any entry by the 'Old Writing Team' has been declared by the editors to be fair game for replacement. Just submit your new entry to Peer Review (saying that there is an old entry by the Writing Team, but you want to replace it) and if it gets through Peer Review it will replace the old one.

- Normal updating is being done on a voluntary basis by Jimi X and Mikey the Humming Mouse, who are both highly experienced sub-editors and authors. Update Headquarters at http://www.bbc.co.uk/h2g2/guide/A496451
explains what they are doing. Since they are doing this in their free time, I don't know how long it takes.

-The third method is more unusual, but I know of two examples where it has worked. I call it 'sidelining'. There was an older entry on 'Opera' (which I didn't like very much!). I put an entry called 'The History of Opera' through Peer Review, and when it was edited, Ashley (I think) changed the name of the older entry to 'A Guide to Opera Plotlines'. It's still there, but most people wanting a link to 'Opera' will now choose my 'History of Opera' entry, rather than the older one, because of the name change.
The same thing happened with the older 'The Pyramids' entry. Gnomon wrote a new entry on 'The Great Pyramid' and suggested that the older entry be changed to 'Numerical Properties of the Pyramids', and it was. Maybe the older Thermodynamics entry could be 'sidelined' as a Beginner's Guide or something like that, and you could produce a Detailed Guide or a Deeper Guide or whatever?


Azara

Good entry, Hell! I suggest that you could point out that, in your footnote definition of an ideal gas, that a gas stops being ideal when the collisions of the molecules (or atoms) stops being elastic, or rather starts being vert INelastic ... that's closer to the physical definition, right? Then again ... maybe for the lay person not familiar with the physics of what constitutes an elastic collision wouldn't get that. I think "stick" is a good enough roughshod definition. I like this entry - it's not a simple subject at all. Thermo gets rather complex in a hurry as many of us remember all too well! That's probably why there are so many EOS (equations of state) out there - some much better at predicting a gas's behavior under various conditions than others. The Virial method is perfect for a gas that someone has already studied (if their data is reliable and there's enough of it!), but that's not always the case, sadly. I've worked with some highly specialized EOS that have little application outside of very specific laboratory settings, heh. Not fun things to use, but the running joke in school was that if you can't come up with a master's thesis why not invent another EOS?

Bossel: Not to speak for Hell, but water can be called water in any of its three main states - we just happen to have given it three different names as a culture thanks to its unique ability to exist in all three main physical states naturally on our planet. I would use caution to differentiate between water vapor and steam, however. Steam and clouds tend to have some suspended agglomerations of water molecules (that's what makes them opaque whereas purely vaporized water is transparent - again, I think this is correct, but I'm not sure - anyone want to clarify the difference between water vapor and steam? ... I should know, given my "Keeper" title, but I admit I've forgotten a LOT). Having said that, as a chemical engineering undergraduate I remember using the term "steam" interchangebly with "water vapor" - probably 'cause it was shorter.

Solsbury: Whether a gas follows the ideal gas law or not depends highly on what the gas is, from a chemical species standpoint (such as, air [a mixture of nitrogen, oxygen mostly, as you probably know of course], carbon dioxide, water/steam, diethyl ether, hydrogen cyanide). Taking your word for it, it doesn't surprise me that air starts to behave non-ideally around that pressure (300 bar) since oxygen is somewhat reactive and is lonely and unhappy with itself, wanting to bond with something else ... just my gut instinct, there, sorry for the silly analogy.

Aren't there many forces acting on the gas molecules, of which the two big ones are electrostatic as well as forces due to sudden acceleration from collisions with other molecules? I thought those two forces combined largely to create the interactions that affect how two molecules will act when they collide, and thus their elastic vs. inelastic collision behavior (or tendency to "stick" or have cohesion). This is where enthalpy, temperature, gibbs free energy, and all that statistical average stuff starts coming into play, right? If I remember correctly, they are all ways of thinking of how energy and matter are fundamentally interacting when small groups of matter (here I'm referring to atoms and/or molecules) collide with each other ... ... I'm forgetting my thermo too easily these days.

Afterthought: I was taught to generally avoid the possible confusion of "pV" being a single symbol by capitalizing "P." Not sure, is that just an American thing, using P for pressure? An engineering thing? I've always capitalized the letter P when referring to pressure. (Possible confusion with the element phosphorus rarely occurs in most circumstances) Speaking of pressure and units, you should try working where I do. The most common units of pressure used here (and by common I mean used with almost daily frequency) are: inches of water column (in. wc), pascals (either as Pa, kPa, or MPa), atmospheres (atm), torr / millimeters of mercury (torr / mmHg), and pounds per square inch (psi). Whew. Did I leave any out? Oh yeah, some people still use bars from time to time (no, not THOSE kind). Unit conversions - ha! - don't talk to me about unit conversions!

Hell, I haven't time to do a detailed examination of this. A quick glance shows it to be good.

What does "Virial" mean? Is it someone's name or is it an obscure word in English or some other language?

You use a raised dot for multiplication in formulas. This looks a bit odd to me because standard British/Irish practise is to use a full stop/period for multiplication.

Latin `vires', means forces. That is so because befor thinking about gases people used this kind of equation to measure ensembles with many many minuscule forces. Equations with such a lot of parameters are called virial equations. For this reason it's called virial.

I've got some loads of stuff to do right now. I'll elaborate a longer reply later.

HELL

PS: About vapour and steam. Clouds are made out of droplets - they are visible, aggregates, liquid. But to get there (in the sky) it had to become gaseous first (invisible). The sun evaporates the sea, forms water gas which is in the atmosphere. At higher altitudes it condensates. This happens with most liquids even below their sublimation points. It's like with phase diagrammes of solids. The air can accomodate a certain amount of a gas before it starts to condensate. Like with a saturated salt solution. Happens with oil, tar and mercury as well. Even solids sublimate. Some few atoms, OK, but nevertheless.... I have included water in the list because it is present in everyday life, even as a gas. Air 'humidity', in the kitchen while boiling or cooking...

Bye - really have no time now. H.

Hi Hell

I read this piece and found it tough-going in places (due to my scientific ineptitude, not because of any aspect of your article!) but worth the effort. Informative, clearly presented and very readable.

I have listed various textual points below. One or two are typos but most are vocab questions. See what you think and take or leave whatever you like. Of course!

Ok, here goes:

>>widely used in trivial everyday thermodynamical reasoning, like for instance for the weather forecast.

- trivial? Well, I agree that this phrase is awkward.

>>thermodynamical - What is the difference between 'thermodynamic' and 'thermodynamical'?

>>humongous - I don't like this word. It is not present in many dictionaries and in my view it is a childish improvisation for 'bigger than huge'. There are lots of other, more widely acknowledged (and in my view more suitable) words.

>>their behaviour with time (dynamic). - Does 'dynamic' mean this? Surely it is more to do with 'matter' and 'motion'?

>>nowadays sound very empirical, far-fetched or out of thin air.

- What do you mean by 'empirical' here. It seems to be a pejorative term, along with 'far-fetched' and 'out of thin air' (is that a gag, by the way? )

>>think-over - I am not familiar with this noun. I guess it must be like a 'make-over' for theories?

>>rendered him a Nobel biscuit - Not knocking the gag () but do you really mean 'rendered' or 'earned'?

>>mearured - typo

>>intesively - ditto

>>as precise as you want - What do you mean by this? Does it also mean 'as IMprecise as you want'?

>>The virial equation - I agree that the word 'virial' needs some explanation.

>>it is totally empirical - you seem to be using this to mean something different to the previous time.

>>summands - I think this word needs some explanation.

>>which are nothing else than - Could you say this differently? It reads awkwardly in English.

>>heart-piece - I know what you mean but I don't think heart-piece is valid in English.

>>gas' behaviours - I realise that the apostrophe is to show a genitive plural but this would be clearer if you rejig the sentence and use 'of gases'

>>but within the temperature range it can be deliberately accurate.

- I don't understand this closing phrase.



You may feel that some of these are points of style that you don't agree with. Fair enough. Overall, I'm sure this will go in. Nice one!

Spiff

just spotted that you have already explained virial. Are you planning to do so in the entry?

I like this entry.

I can also remember Thermo as an engineering student and I must say, Hell, that if my lecturer had been as clear as you in this article, Thermodynamics would have been a lot more interesting.

Nice job, and a handy reference.

Madent

OK... So here I go.

Solsbury: I'll try to include some values to demonstrate the inaccuracy. (It will take one day or so.) Good idea! Thanks.

Azara: Thank you a lot. I'll keep that in mind

JD: Elastic Inelastic - That's jargon, I'm not sure if everyone will understand this, I'll add the two words for completeness though. Steam / Vapour: See above. Enthalpy, interactions etc. Yes, there's quite a lot of energy in there, that's the reason why a refrigerator works. (If it were an ideal gas we could not built refrigerators as easy as that). P or p: In our institute (and in the literature I am familiar with) we use p. I don't care if other people use 'P' as long as it is clear what we're talking about. I think the difference between p and P is that P is used for macroscopic values and p for microscopic, but then again the usage got somewhat blurry. And yes: Pressure has the most stupid and incoherent units. I like N/m^2, bacuse I can imagine it well, because it's metric and SI. Conversion of units... There's an entry about that somewhere in the guide... I'll add that lik when I find it.

Gnomon: I'll include the explanation to virial in the entry, thanks for pointing that out. Using dots... Hmm, I like 'em. But I could of course change it easily. What do others think?

Spiff: First sentence: OK It's awkward. I just didn't want to start the entry abruptly. I'll think about some other formulation. Thermodynamic, OK (I speak 4 languages sort of fluently, sorry, sometimes they get mixed up). Humongous was in there for the giggle value, I heard it often and saw it in some pop-science articles, so I thought it was OK... But I'll try something else (But not everything MUST be in a dictionary, must it?).

Spiff (cont'd): dynamic = with time. It has to do with matter and motion because these happen with time. Empirical: You are right: This word has some negative value in the scientific community. In this case (Eqn of state) there's no way out though, so...What I meant was: Even though it is empirical, out of thin air and far-fetched, there's nothing better than it. (And no, this time it was not a gag). Think-over... Hmm isn't there the expression "I need to think it over"? Meaning: "Hmm... Let us look at that again."?

Spiff (cont'd): Earned... OK. Typos... OK. Summands...? I thought this was the official term for terms between '+'s? Maybe 'nothing but'? heart-piece: why not? Maybe cardinal piece? Central piece? Fundamental?... I'll use gases' (genitive). Deliberately accurate: You can make it as accurate as you want, all you have to do is find the 2nd, 3rd, 4th etc.. constants. The more constants the better. But it has little meaning as it is very specific for a certain gas and a certain temperature.

Madent: Thanks, I am flattered.

See you all later (I'm doing the changes in a while.)

Thanks a lot for all the comments.

HELL

Hell, now I have had time to read your entry properly. There are a few typos and points of grammar which I will point out in my usual way. The only thing I find wrong with the content is that it starts too abruptly. There needs to be an even gentler introduction.

Now for the nitpicking:

stupefying variety ... I'm not entirely happy with this because in English variety can also mean "type". Is there another way of saying it?
unthinkable --> unthinkably
rubbing sticks against wood ... while this is accurate, the normal expression is "rubbing sticks together"
with time (dynamic) ... the (dynamic) looks a bit lost here. Maybe you could just omit it.
the motor of a car --> the engine of a car
central piece --> centrepiece (this occurs in two places)
phone-book like --> phone-book-like
pointlike --> point-like
eachother --> each other
repulse --> repel
idael --> ideal
Use a semicolon rather than a comma in two places:
"for a gas, it is totally empirical"
"not constant, their value"
deliberately accurate ... I have no idea what this is intended to mean. I think it might be a mistranslation from whatever language you think in.

Good work, once again!

Hmmm, Gnomon has said pretty much everything I was going to... if you don't mind, can I suggest a slight re-write of the last couple of sentences? Something along the lines of:

"The third form is the 'virial' equation which is specific for one type of gas within a certain temperature range. The parameters required for each gas and temperature can be found in tables, and are discovered by careful experimentation. The virial equation is somewhat more difficult to handle from a mathematical point of view, but within a specific temperature range it can be as accurate as is desired."

Incidentally, my own view is that the introduction is fine. You could put some waffle in at the start, but I don't think it needs it.

Intro looks better to me, now. Haven't much time, so got to

I don't get this at first reading. However, I suspect I will in subsequent reading, and this is why I'm posting; I think the details of quite a complicated concept have been presented in a way that us laypeople can find accessable.

Well done for that

There seems to be a fair amount of confusion with Hell's phrase, "deliberately accurate." I think what was meant to be conveyed was a an implication of how accuracy is contrived deliberately by many equations of state.

By the way Hell, you should probably change the heading of the Virial Equation section to "as accurate as you want" instead of "... precise..." as the second one isn't technically the right term. Precision, of course, is more a measure of how well an instrument performs its measurements (like how many significant figures it is capable of), while accuracy is how well a model or prediction holds up to actual observed data.

In that light, it is plain to see that the Virial equation is actually a DESIGNED accuracy, whereas usually accuracy is a measure of how well a hypothesis holds up and is not designed at all - one might liken it to a situation where one was allowed to grade one's own exam and change the answers after one had seen the answer key. Empirical equations are only as good as the data used to determine their constants, so the answer is known (or measured) then the equation is made to fit it. One may exhaustively study and collect data on a specific gas at a very narrow temperature range and arrive at a virial equation that is so accurate as to be limited by the precision of the instruments used to measure the thermodynamic variables. I think that's what was meant by "deliberate accuracy," because it's a bit of a contrived thing from a classically scientific standpoint. That is, instead of coming up with a mathematical expression based on a hypothesis, the virial equation simply recognizes that the bahavior of the data can be very accurately modelled using a bland sort of equation IF one spends enough time to experimentally determine the applicable constants of the equation.

All that is not quite how classical scientists would like to think, at least in my experience. The correct application of the scientific method, as a classical scientist might think, would eventually lead to a theory that explains things with 100% accuracy without the usage of empirical methods. In fact, a fair definition of the term "empirical" could be, "relying on observation or experiment alone, without the use of hypothesis or theory." From an engineering or applied scientific standpoint (traditionally more practical than pure science), empirical methods are fine, and in many cases (like thermodynamics) are all we have. For many scientists, however, empirical equations and formulae are simply "quick and dirty, but not substitute for the real thing." The ultimate quest or goal is to not have to rely on empirical data, though if one reads Dr. Hawking or more appropriately Gödel at all, one might suspect that such complete knowledge is in fact unobtainable.

I think I've rambled on enough here, heh. Just wanted to put forth the idea that maybe "deliberate accuracy," while a confusing phrase in English, goes some way towards expressing the mild feeling of disdain some scientists might have for some equations of state. Of course, this is all my own personal musings and not meant to taken as gospel, internally, or precisely accurate in any respect.