Are the gas laws compeletely true?

[dauto]

Why are you trying to defend that "nonsense" word?
Of course one would need to be 'cautious' in applying the laws of Gravity to the Atmosphere because they would be inadequate. You said it yourself. Likewise for the Gas Laws. This would appear to be a majority view.
Can we drop it now?

I don't think the idea that the laws of gravity might be inadequate constitute a majority view. Not even close. I already apologized for using the word "nonsense" because I think politeness is important. That doesn't mean that the post I was responding to was correct. It was most definitely not correct because it turns out that the ideal gas law is actually very accurate everywhere on Earth's atmosphere. even at places where water is changing states. That's just the truth. The ideal gas law will give you at least 3 correct significant digits. If you just plug in the correct temperature, pressure, and volume, the law gives you the correct number of moles of gas inside of that volume to high accuracy and that's all that law is meant to do.

 

[sophiecentaur]

I don't think the idea that the laws of gravity might be inadequate constitute a majority view. Not even close. I already apologized for using the word "nonsense" because I think politeness is important. That doesn't mean that the post I was responding to was correct. It was most definitely not correct because it turns out that the ideal gas law is actually very accurate everywhere on Earth's atmosphere. even at places where water is changing states. That's just the truth. The ideal gas law will give you at least 3 correct significant digits. If you just plug in the correct temperature, pressure, and volume, the law gives you the correct number of moles of gas inside of that volume to high accuracy and that's all that law is meant to do.

And how does that, alone, help you in predicting what will happen in the atmosphere? I think you are having a problem with comprehension here. It was perfectly clear to most of us what was meant by 'that post'. You clearly mis-interpreted it and can't bring yourself to say so.

 

[dauto]

And how does that, alone, help you in predicting what will happen in the atmosphere? I think you are having a problem with comprehension here. It was perfectly clear to most of us what was meant by 'that post'. You clearly mis-interpreted it and can't bring yourself to say so.

Nah... I think you're the only one talking about using equations alone. The statement I was responding to clearly said you must be careful applying the ideal gas law to Earth's atmosphere. Turns out that you can always apply the ideal gas law to Earth's atmosphere with good accuracy so the statement was misleading. I pointed that out.

 

[voko]

On agreement that the ideal gas law does not preclude a change in the amount of matter. that's why n shows up in there so that the amount of matter (and its possible change) is taken into account.

So how can I apply the ideal gas law to 1 kg of water at T = 200 K and P = 1 atm? What volume does that occupy?

 

[sophiecentaur]

Nah... I think you're the only one talking about using equations alone. The statement I was responding to clearly said you must be careful applying the ideal gas law to Earth's atmosphere. Turns out that you can always apply the ideal gas law to Earth's atmosphere with good accuracy so the statement was misleading. I pointed that out.

Perhaps if that original post had said "there's more to it than just the gas laws", (which is how I took it) we wouldn't be arguing. I think we agree that there gas laws aren't enough.

 

[Chestermiller]

So how can I apply the ideal gas law to 1 kg of water at T = 200 K and P = 1 atm? What volume does that occupy?

Dear Voko,

This is kind of an ambiguous question, so maybe you can help us out and provide some clarification. Thanks.
1. Are you referring here to water ice crystals in the atmosphere at 200K? If so, the ideal gas law doesn't apply to them.
2. When you say P = 1 atm, are you talking about the total pressure of the air, or are you referring to the partial pressure of the water vapor in the air? Of course, the partial pressure of the water vapor in the air at 200K can't be much higher than the equilibrium vapor pressure of water vapor over ice at 200K, but, if you know the partial pressure, you can use the ideal gas law to accurately calculate the concentration of water vapor in the gas phase in m³/kg.

Please help us by stating your question just a little more precisely. Thanks.

 

[dauto]

Perhaps if that original post had said "there's more to it than just the gas laws", (which is how I took it) we wouldn't be arguing. I think we agree that there gas laws aren't enough.

Yes, I agree with that.

 

[voko]

Dear Voko,

This is kind of an ambiguous question, so maybe you can help us out and provide some clarification. Thanks.
1. Are you referring here to water ice crystals in the atmosphere at 200K? If so, the ideal gas law doesn't apply to them.
2. When you say P = 1 atm, are you talking about the total pressure of the air, or are you referring to the partial pressure of the water vapor in the air? Of course, the partial pressure of the water vapor in the air at 200K can't be much higher than the equilibrium vapor pressure of water vapor over ice at 200K, but, if you know the partial pressure, you can use the ideal gas law to accurately calculate the concentration of water vapor in the gas phase in m³/kg.

Please help us by stating your question just a little more precisely. Thanks.

Those are interesting questions, given your previous statement: "I might add that, even for pure water vapor at pressures up to 10 atmospheres, the ideal gas law accurately describes the behavior (to within about 5%)."

1 atmosphere is certainly less than 10 atmosphere, yet now you say that "the ideal gas law doesn't apply".

 

[Chestermiller]

Those are interesting questions, given your previous statement: "I might add that, even for pure water vapor at pressures up to 10 atmospheres, the ideal gas law accurately describes the behavior (to within about 5%)."

1 atmosphere is certainly less than 10 atmosphere, yet now you say that "the ideal gas law doesn't apply".

Here's how it works. For a single component H2O system (pure water), if the pressure is 1 atm., water vapor (i.e., a gas phase) can be present only at temperatures greater than 100 C. Below this temperature, all the water will condense to liquid water or ice (depending on the temperature). So, if you have liquid water or ice only, you don't expect them to be able to be described by the ideal gas law. Otherwise it would be called the ideal liquid law or the ideal solid law. At temperatures above 100C, if the pressure of the system is ≤ the equilibrium vapor pressure of water at that temperature and also less than 10 atm., the water will be purely in the gas phase and will satisfy the ideal gas law to a good approximation.

Now let's consider a multicomponent gaseous system like air (where H2O is not the only chemical species present). In atmospheric air, water vapor is only one component of the gas phase, and its mole fraction is everywhere less than 0.03. So its partial pressure at sea level in the gas phase is less than 0.03 atm. At locations in the atmosphere where the temperature is 200K (i.e., close to the tropopause), the equilibrium vapor pressure of water is only about 0.000002 atm, while the total air pressure at these locations is on the order of 0.1 atm. At these locations, if ice crystals are present, we expect the partial pressure of the water vapor in the air to be about 0.000002 atm, but, if ice crystals are not present in the air, the partial pressure of the water vapor can be somewhat less than 0.000002 atm. In either case, the gas phase at these locations will behave as an ideal gas, both with respect to the overall gas mixture as well as to the water vapor. In applying the ideal gas law to the water vapor in a gas mixture, however, one uses the partial pressure of the water vapor, not the total pressure.

 

[voko]

Here's how it works. For a single component H2O system (pure water), if the pressure is 1 atm., water vapor (i.e., a gas phase) can be present only at temperatures greater than 100 C. Below this temperature, all the water will condense to liquid water or ice (depending on the temperature). So, if you have liquid water or ice only, you don't expect them to be able to be described by the ideal gas law. Otherwise it would be called the ideal liquid law or the ideal solid law.

I think you are too restrictive by saying "only" there. A mixture of phases at some particular temperatures and pressures would also give the ideal gas law a hard time.

Yet some people claim that the ideal gas law works even when water changes states. It is about time you guys made up your minds.

 

[Chestermiller]

I think you are too restrictive by saying "only" there. A mixture of phases at some particular temperatures and pressures would also give the ideal gas law a hard time.

Yet some people claim that the ideal gas law works even when water changes states. It is about time you guys made up your minds.

I never made such a claim, so please don't lump me in.

In terms of a mixture of phases, what I'm saying is that the ideal gas law describes the gas phase (i.e., excluding the volume of the solid or liquid) if you use the partial pressure of each species when you apply the ideal gas law to that species in the gas phase. It also describes the gas phase as a whole at the total pressure of the system.

 

[russ_watters]

I think you are too restrictive by saying "only" there. A mixture of phases at some particular temperatures and pressures would also give the ideal gas law a hard time.

Yet some people claim that the ideal gas law works even when water changes states. It is about time you guys made up your minds.

Depends what you mean by "a hard time". A great deal of thermodynamics involves analyzing multiphase mixtures and the ideal gas law is a very important part of the analysis.

For example, at a given temperature there is a certain vapor pressure of water - let's say saturated for simplicity. If you reduce the temperature, you get a new vapor pressure. Comparing the states with the ideal gas law tells you how much was converted to liquid water.

The ideal gas law rarely the only tool used in a thermo problem, but it is very often an important one. Not being the only tool, however, doesn't to me constitute "a hard time".

 

[voko]

I never made such a claim, so please don't lump me in.

Then I don't understand what you are debating here. If you agree that the ideal gas law does not apply "even when water changes states", just say so and let's be done with that.

You keep re-iterating trivia of the behavior of water vapor that does not change states, but that is beside my point.

 

[Chestermiller]

Then I don't understand what you are debating here. If you agree that the ideal gas law does not apply "even when water changes states", just say so and let's be done with that.

You keep re-iterating trivia of the behavior of water vapor that does not change states, but that is beside my point.

I'm sorry my comments have been so frustrating and trivial to you. You and I seem to be on different wavelengths in this discussion. The discussion has become too contentious for me, so I am withdrawing from further postings in this thread. I hope that other readers of the thread have been able to relate more to what I have been saying. No hard feelings.

Chet

 

[voko]

The ideal gas law rarely the only tool used in a thermo problem, but it is very often an important one. Not being the only tool, however, doesn't to me constitute "a hard time".

My point is that the ideal gas law cannot describe phase transitions at all. Those are described by more accurate equations of state, which then can be used for the gas part just as well, making the ideal gas law fully redundant.

My stronger point is that if we treat the system as a black box (say a vessel at constant pressure and varying temperature), then the ideal gas law fails completely.

In the broader context of this entire thread, there was a statement that the ideal gas law should be applied with caution to the atmosphere. That was denounced as nonsense, the ideal gas law was said to describe the atmosphere very accurately and it was proclaimed correct "even when water changes states". While it is precisely here that caution must be exercised, because liquid and solid phases have to be dealt with differently, so the ideal gas law does not in fact describe all the atmosphere.

 

[russ_watters]

Volko, the first usage of "nonsense" was dealt with and over when you then said this:

Ideal gas law applies when water changes states? Who mentioned "nonsense" in this thread?

It was no less offensive (as was pointed out before you said it) for you to use it and making a point by asking a vague, rhetorical question is not helpful either.

Again, the bottom line is still that the ideal gas law is very useful in describing the atmosphere EVEN WHEN PHASE TRANSITIONS OCCUR.

Both the first usage of the word and yours were overzealous, but more to the point, your statement that the ideal gas law can't help at all with a phase transition is wrong.

 

[russ_watters]

Sample problems that can be solved primarily by using the ideal gas law (or derivative of it):

1.
1000 cubic feet of air enters an air conditioner at 90F and 50% RH and leaves at 55F. How much water vapor condensed into water?

2.
An air mass of 0.1 cubic miles volume at 80F and 50% RH blows over a large lake and is cooled to 70F by evaporating water. What is the new volume, RH and how much water evaporated from the lake?

Even with simplifications and shortcuts, both of these involve finding a mass of water vapor using absolute humidity. Absolute humdiity is calculated using the ideal gas law (even if you get it from a table, that's how it got into the table). See here:

Two basic laws apply to the air and vapor mixture that make our calculations possible. First, within the range of comfort air conditioning, the mixture follows the ideal gas laws...

Second, the gases follow Dalton's law of partial pressures.

http://siglercommercial.com/wp-content/uploads/2013/01/Psychrometric-TDP-Preview.pdf

So I would go so far to say that the ideal gas law is an essential part of atmospheric analysis for a wide variety of problems, if not most problems. In my line of work (heating and air conditioning), essentially all problems involving the thermodynamics of humid air utilize it.

 

[voko]

your statement that the ideal gas law can't help at all with a phase transition is wrong.

I fail to see how the ideal gas law can help with phase transitions. They do not manifest themselves in the law in any way. It was said by others, which I did not debate, that the residual gas is still described by the ideal gas law. But one needs something else, not the ideal gas law, to determine how much of that residual gas remains. I do not perceive that as "helping with a phase transition". It only helps with the residuals.

Or am I really missing something very big?

 

[russ_watters]

I fail to see how the ideal gas law can help with phase transitions. They do not manifest themselves in the law in any way. It was said by others, which I did not debate, that the residual gas is still described by the ideal gas law. But one needs something else, not the ideal gas law, to determine how much of that residual gas remains. I do not perceive that as "helping with a phase transition". It only helps with the residuals.

Or am I really missing something very big?

Did you see the sample problems I posted? For the first one, "How much of that residual gas remains" is precisely what the ideal gas law gives you when you plug in the new temperature and partial pressure.

 

[voko]

Did you see the sample problems I posted? For the first one, "How much of that residual gas remains" is precisely what the ideal gas law gives you when you plug in the new temperature and partial pressure.

Is the partial pressure given by the ideal gas law? I do not think so. You need something else to know it. This is what I have been saying all along.

 

[russ_watters]

Is the partial pressure given by the ideal gas law?

No.

You need something else to know it. This is what I have been saying all along.

No, your claims have gone far beyond that. There is a big difference between saying it is the only tool needed (which no one has claimed) and saying it can't be used at all (which is what you claimed).

 

[sophiecentaur]

56 Posts! and all because someone said you need to be cautious in practical circumstances.

 

[dauto]

Is the partial pressure given by the ideal gas law? I do not think so. You need something else to know it. This is what I have been saying all along.

Off course not. For finding the partial pressure you should use the Clausius–Clapeyron equation.
Where did you get the idea that I (or anybody else here) was saying you could solve a problem with just one equation? You may have to use more than one equation. My point is that the ideal gas law is one of those equations, and even if there is a phase transition, it will be accurate enough pretty much everywhere in the Earth's atmosphere, specially considering that the water vapor pressure is just a small component of the total atmospheric pressure. That may seem surprising since we all are supposed to have learned long ago that the ideal gas law does a poor job near transitions.

 

[dauto]

56 Posts! and all because someone said you need to be cautious in practical circumstances.

I think we've been talking past each other for most of those posts...

 

[K^2]

56 Posts! and all because someone said you need to be cautious in practical circumstances.

That's a trend around here. Almost every thread that should end with the first reply post being, "No," seems to run on for pages and pages.

 

[voko]

No, your claims have gone far beyond that. There is a big difference between saying it is the only tool needed (which no one has claimed) and saying it can't be used at all (which is what you claimed).

I have checked all my posts in this thread and I do not believe I ever said it could not be used at all. I explicitly agreed that it could be used for gas residuals. But not for the whole system, and some other law is required to find out the amount of the gas residue.

It seems to me that whether one can say the ideal gas law applies or does not in this situation is a matter of opinion. I have expressed my opinion, others have expressed theirs. If I have offended anyone by any figure of speech, I apologize. I have to excuse myself from further participation in this debate.

 

[russ_watters]

I have checked all my posts in this thread and I do not believe I ever said it could not be used at all. I explicitly agreed that it could be used for gas residuals. But not for the whole system, and some other law is required to find out the amount of the gas residue.

You said it could not be used at all when dealing with a phase transition. That's the scenario we are discussing:
"...the ideal gas law cannot describe a phase transition at all."

You repeated several iterations of that statement. What you are missing is that the ideal gas law doesn't have to describe the transition itself to provide an insight into what happened in the transition.

It seems to me that whether one can say the ideal gas law applies or does not in this situation is a matter of opinion.

No, it really isn't. Utilizing a particular equation to solve a problem will either give a right answer or a wrong answer (to a certain precision). I provided examples of problems that apply here and you ignored them.

There is very little in science that is a matter of opinion.

 

[klimatos]

Most gas laws require that conditions of equilibrium exist (if not throughout the process, then at least at the beginning and end of it). Since the Earth's atmosphere in never even close to a condition of equilibrium, one must be very, very cautious in trying to apply laboratory-valid gas laws to the free atmosphere.

I have been out of town for the last week, and never imagined the fuss that this simple caution would produce. I was referring to non-equilibrium conditions in the free atmosphere--not in the laboratory. The image I had in mind (but, unfortunately did not specify) was the violent and changeable winds accompanied by condensation that can be found in thousands of thunderstorms that are occurring even as you read this post.

If you have an equation of state that accurately relates ambient pressures (including wind pressures) to temperatures (both at the surface of the condensing droplet and in the air between) that is valid under these circumstances, I would dearly love to see it.

I am not unfamiliar with the ordinary gas laws (Boyle's Law, Charles Law, etc.), which is what I had in mind when I wrote the post. I have just reviewed them, and--sure enough--most of them require conditions of equilibrium to be valid.

What did I say that was so contentious?

 

[Chestermiller]

I have been out of town for the last week, and never imagined the fuss that this simple caution would produce. I was referring to non-equilibrium conditions in the free atmosphere--not in the laboratory. The image I had in mind (but, unfortunately did not specify) was the violent and changeable winds accompanied by condensation that can be found in thousands of thunderstorms that are occurring even as you read this post.

If you have an equation of state that accurately relates ambient pressures (including wind pressures) to temperatures (both at the surface of the condensing droplet and in the air between) that is valid under these circumstances, I would dearly love to see it.

I am not unfamiliar with the ordinary gas laws (Boyle's Law, Charles Law, etc.), which is what I had in mind when I wrote the post. I have just reviewed them, and--sure enough--most of them require conditions of equilibrium to be valid.

What did I say that was so contentious?

See the following reference:
Microphysics of Clouds and Precipitation (Atmospheric and Oceanographic Sciences Library) Paperback
by H.R. Pruppacher (Author) , J.D. Klett (Author)