# I Gas Law applying to air vs water vapor

Tags:
1. Dec 7, 2016

### zanick

Say we have a tire filled with air (equal to ambient air surrounding it in every way). pressure on the gauge is 0. Then, we pressurize it to 1 ATM (15psi). If we heat the tire , the air will be heated and expand based on gas law, or is there a factor that changes it based on the air's water vapor content.
Example: we heat the tire to 150 degrees and the pressure goes up 5psi.

Now, what if we use dry air or Nitrogen from a bottle. will the pressure rise the same?

since filling the tire with air with a water vapor content, could condense the water vapor as the pressure rises. if so, then if the tire is heated, then the water that has condenced could also turn to vapor at a specific tempurature..... of so, its volume would increase by 1700times and could raise the pressure in the tire to higher than it was for an equal tempurature with dry air or nitrogen.

So, the quesion is, does air with water vapor follow Gas Law, until there is some kind of condensation of the water vapor?

thanks

2. Dec 7, 2016

### Cutter Ketch

First before I say anything to muddy the water let me say that your instincts are correct and nonideal gas law stuff will happen and the nonideality will be particularly dramatic if there is a phase change such as condensing water.

Now a quick comment not exactly in answer to the question. No real gas behaves as an ideal gas for two reasons. First the molecules take up some space. The first correction to the ideal gas law is to reduce the volume by the amount the molecules would take up if they were closely packed together (ie. solid). Second, the molecules have some attraction to each other and they stick together a bit. So Helium is a pretty good ideal gas because the molecules take up little space and they don't stick together at all. The vapor above the liquid of some giant organic molecule is a terrible ideal gas both because it's huge and the molecules are so sticky they'll form a liquid at the current temperature and pressure.

Now, in your tire dry nitrogen is a pretty good ideal gas. The dimers take up some of the volume, but not much, and N2 is so unattractive to itself that it doesn't liquefy until 77K. Oxygen dimers will react chemically with practically everything, but they are not very attractive to each other or nitrogen and the rubber is already fully oxidized. So dry air will make a relatively good ideal gas.

Water vapor even before it condenses will drive the gas away from ideal gas behavior. How much? Well actually not enough for you to worry about, but the molecules stick together more, and that affects the ideal behavior.

If the water vapor crosses a threshold and starts to condense the phase change will greatly affect the ideal gas behavior. In particular the volume vs pressure is stuck

3. Dec 7, 2016

### Simon Bridge

If you pressurize a tyre to 1atmos guage from 0 guage, then the gas pressure inside is 2atmos.
The rubber stretches until the restoring pressure matches the guage pressure.

Water vapour suspended in air is not an ideal gas no. Neither is air.
There is also an issue that water vapour can condense in some situations. A phase change will mess with the PV diagrams.

Nitrogen is not an ideal gas either ... but it is more closely ideal than dry air which is better than normal wet/dusty/dirty air.
If you used clean dry helium you'd get a better match to the ideal gas law.

If the tire contains liquid water - changing conditions can make it vaporise - increasing the pressure by lots yes.
How far the tyre expands depends on the materials it is made out of.

To answer your question: "no". IRL do not expect wet air to follow the ideal gas law.
There are rules of thumb for handling wet gasses - involves humidity, dew points, and vapour pressures.

4. Dec 8, 2016

### Staff: Mentor

What makes you think that the water vapor will condense?

Incidentally, treating the mixture of air and water vapor at 2 atm as an ideal gas is a really good approximation.

5. Dec 8, 2016

### zanick

I understand that the absolute pressure is 2 atmos if the gauge says 15psi. (ambient plus gauge pressure) im not so much concerned with the amount of tire expansion, as i am with the pressure in the tire, for racing engineers, a certain pressure makes the tire perform better. the question really revolves around predicting the pressure rise in the tire, based on gas law....... it seems that water vapor and air , both not being ideal gases might expand at the same rate until the pressures are much higher (well beyond the 30 to 45psi pressures we are talking about here)

you mention "changing conditions" and increasing the tire pressure can vaporize water...i was thinking the opposite. with pressure change going from ambient to 15 to 30psi, wont the water vapor condense at a higher pressure, just as it vaporizes at lower pressures depending on the temp? or were you referring to a higher increase in pressure that creates heat that vaporizes water.. i was thinking along the lines of the opposite. increasing the pressure in the tire, so that the water vapor condenses. then, when the heat increases in the tire, to over boiling point (as well as the pressure increasing due to P/V ) the water vaporizes and adds to the pressure.

6. Dec 8, 2016

### zanick

Thanks for the reply... so, it sounds like my assumption that in the 1-2-3 atm range, water vapor and air act near the same?
i was thinking that the water vapor would condense as the pressure increases following the gas law graphs. (and some intuition that might be wrong here) If there was some water vapor in the tire, by adding pressure doesnt that condense the water vapor if the dew point is hit.
here is the scenario. you add pressure to a tire with a pump using air. humidity outside is say, 80%... temp is 68 degrees. you raise the pressure to 30psi gauge pressure (which is 45 psi absolute) there is some temp rise initially, but it goes back to ambient over time... could the vapor in the air condense, or is the pressure still too low? then, the tire is run on a race track where temps rise to the 220F range, and the inner rim are seeing 250F. since the higher pressure resists boiling, but it still boils at 250F when in contact with the rim that vapor would then raise the pressure higher than if the air had no water vapor content to begin with.
at the track, many see this differential pressure as being 30psi to start, going to 38psi when hot, but with dry air or Nitrogen, the delta is only 5 degrees, going from 30psi to 35psi when hot.

7. Dec 8, 2016

### zanick

Thanks for the detailed response and theory at the molecular level... thats interesting and havent heard it described that way. also interesting that water vapor and air seem to act similar in certain temp and pressure ranges as i gather from your statement . we are talking about 70F temps, standard day, and pressures up to 45psi absolute. the question really becomes, when racers at the track , see temp variation of their tires which are greater with air vs nitrogen, is it due to the water vapor raising pressure at a disproportional rate vs dry air or nitrogen,or is it the water vapor condensing upon pressurizing the tire, which when heated , vaporizes and raises the pressure to a higher level than dry air or Nitrogen? If so, would this happen only on a race tire, and not on the street, because street temps are much lower (140F range) which wouldnt boil the water , especially since its under pressure of 30 to45 PSI absolute. (2-3 atm)

8. Dec 8, 2016

### Cutter Ketch

So basically you have two cases. In the first you add humid air at effectively constant temperature while constraining the system to essentially constant volume. The pressure increases, and at a particular pressure the water will begin to condense out. At what pressure it begins to condense out depends on the relative humidity of the air that is being added. If the air is at 100% relative humidity the water will begin to condense out with any pressure increase. Lower humidity will condense at higher pressure. The condensation happens when the partial pressure of the water reaches the vapor pressure of water at the temperature. This means the condensation point is inversely proportional to the relative humidity. For example 50% relative humidity at 1atm will reach 100% relative humidity and begin condensing out water at two atm.

In the second case you have a sealed system with more or less constant volume being heated by racing. Both the temperature and the pressure increase. Ideally they are proportional, but what happens to the water? The vapor pressure (not the pressure of the vapor, but rather that pressure at which the vapor would condense if it were achieved) actually drops with increasing temperature, but only very slowly (see tha Antoine equation). This is one way to think about boiling water. You increase the temperature until the vapor pressure falls below 1 atm. However, since the pressure is increasing inversely with temperature and the vapor pressure is only changing slowly, the pressure increase wins. That means that as the temperature and pressure increase if you haven't already reached the condensation point you may get there and start to condense water (yes you had it right and whoever said the opposite above was mistaken)

9. Dec 8, 2016

### Staff: Mentor

Zanick:

You seem very confused about all this. We can remove all your uncertainty by quantitatively modelling this. I can define a quantitative problem and lead you through the calculation. Are you game to try?

Chet

10. Dec 10, 2016

### zanick

that makes sense............thanks!

11. Dec 10, 2016

### zanick

yes......... I'm game.....

12. Dec 11, 2016

### Staff: Mentor

Consider a tire with an internal volume of 1.2 ft^3 that is currently at a pressure of 30 psig (44.7 psia) and 70 F. The tire was originally pressurized starting with air at 70 F, 14.7 psia, and relative humidity 80%. What is the vapor pressure of water at 70 F. For a relative humidity of 80%, what was the partial pressure of the water vapor in the air that was pumped into the tire? What was the mole fraction of water vapor in the air that was pumped into the tire?

To be continued.

13. Feb 2, 2017

### luminoussands

Hello, we are having a problem agreeing in a Volvo forum regarding the so called benefits of nitrogen filled tires.

Supporters of nitrogen (with no evidence) claim tires have less fluctuation in tire pressure with a change in temperature, have less seepage of air through the rubber of the tire and have less corrosion of the tire rim.

Opponents, like myself think the change in tire pressure for air versus pure nitrogen to be minimal, think it's not true that a lower molecular weight molecule would seep through rubber more easily and think corrosion of the tire rim is absolute nonsense since the outer rim is exposed to the elements all day long and does just fine.

Through physics can we prove which argument is right?

Thanks for the insight.

14. Feb 4, 2017

### Simon Bridge

No you can't.
You have a choice of physical models which may or may not apply in different situations.
Even if everyone agreed on a model to use, that does not make the conclusions drawn from the model correct.
The way to determine if something is true in reality is to conduct experiments.

One of the issues you will have is on the definition of "minimal" ... there may be a real verifiable advantage that may even be among the advantages supposed by proponents, but they are not big enough to be worth the cost except in specialist areas. My understanding is that a lot of NZ truck companies use nitrogen to fill their tyres becuase they see a benifit on their bottom line ... it's cheaper to run the trucks that way, when that is the only thing they change. I have not seen the data and am not aware of any peer-reviewed research either way.

But you don't need any. Skepticism is your freind here:

The proponents are the ones making the positive claim, so they have the burden of proof. Just tell them you don't believe them, and ask for the evidence that they use to support the claim. It is thair job to do the work, not yours.

If they ask you to prove it does not work, tell them that is called, "shifting the burden of proof" ... as long as you do not claim that you know it does not work, you have no burden. If they imply that being unable to demonstrate their claims false means they are justified to think they are true, that is called, "argument from ignorance".