More noise from your Z06 and Nitrogen Tires

[Dick S.]

Re: Questions about physics

OK We're making progress.

The issue that we apparently disagree on is whether or not water vapor reacts as an Ideal Gas. I claim, by the examples and published tables, that it is not. Only when the PT relationship is above the boiling point, and the gasseous mix has zero relative humidity, will it, but this occurs at temperatures we hope never to see in our race tires.

So lets focus on this issue. You indicate that the non-linear change in pressure is minimal and due to volumetric changes from the condensation and probably not detectible with a pencil tire gauge. Yet, with the example of the pressure cooker, as anyone who has ever used one can attest, the pressure changes are substantial as the water nears and exceeds 200 degrees, just as the charts of vapor pressure show. As much as a 30x increase from ambient to 212 F. We definitely have not altered enough liquid to vapor volume to explain this. How can this happen if as you claim, water vapor reacts as an Ideal Gas?

Only after relative humidity drops to zero, either by the elimination of water vapor due to drying and evacuating methods, OR the PT relationship is greater than the boiling point causing all of the vapor to transition to gas, will the resulting mix act as an Ideal Gas.

[Duke W.]

Re: Questions about physics

A pressure cooker creates a two-phase mixture (saturated steam) until all the liquid water is converted to vapor (gas) phase. The temperature of the water and water vapor (at constant pressure) will not increase until all the water evaporates and at that point it becomes superheated steam and more heat addition will increase temperature and pressure.

A pressure cooker is essentially a miniature version of a boiler such as is found on old steam locomotives and steam ships, steam power plants, and nuclear powered aircraft carriers and submarines.

Constant pressure is key since any pressure cooker or boiler has a safety valve that prevents pressure from exceeding the design limit, so if your boiler is designed for 300 psi and has no superheater (or your pressure cooker is designed for 3 psi), a glance at the steam tables tells you what the temperature will be. It's been a zillion years since I saw a pressure cooker, but I remember making hard boiled eggs with then when I was a kid. I can't imagine the safety valve was more than a few psi, which let the temperature get somewhat above 212F, and that cooked the eggs faster than boiling them in an open pan.

Does superheated steam behave approximately as an ideal gas? Essentially that's what water vapor in unsaturated air is - superheated steam!

Duke

[Mark K.]

Re: Questions about physics

The way to calculate the differences between ideal gas assumptions and the real properties of nitrogen (the main component of air) and water vapor is to start by calculating the pressure differential of an ideal gas at 2 different temperatures (a typical high and low range for tire operation in this case)and then, using empirical data, calculate the difference in pressure for each of the actual gasses.

One initial assumption is that the system within a tire is a closed system – no matter can be transferred in and out of the system (but energy can affect the system).

An Ideal gas formula (as we know) is: PV=nRT where the universal gas constant R = 82.06 (cm*3 atm)/(mole deg K).

An ideal gas ( 1 mole) thus at 3 atmospheres (the approximate temperature in a tire at 0 degC =
(82.06)(273.15K)/(3 atm) = 7.47156 liters

Assuming that the tire volume remains constant, an increase in temperature to 100 deg C (or the temperature of boiling water) will increase the ideal gas pressure (using the same formula) from 3 atm to 4.09830 atm. This is thus the range to compare the ideal gas pressures to the real gas pressures.

Real gas deviates from ideal gas by understanding the compressibility factors for the specific gas. Empirical factors for water vapor and nitrogen have been developed for the “van der Waals” equation which in an analytical real-gas equation of state.

(P +[a/V*2])(V-b)=nRT

If again we assume we are working with one mole of gas the “n” falls out.

a for nitrogen is 1.35 x 10 *-6 /(cm*6 atm mol*-2), b for nitrogen is 38.6 /(cm*3 mol*-1)
a for water vapor is 5.47 x 10 *-6 /(cm*6 atm mol*-2), b for water vapor is 30.5/(cm*3 mol*-1)

Solving for P at constant volume for the range of temperate 0 to 100 deg C (or 273.15 to 373.15 deg K)

Nitrogen at 0 deg C = 3.0156 atm, at 100 deg C = 4.1196 atm
Water vapor at 0 deg C = 3.0123 atm, at 100 deg C = 4.1151 atm

Notice first that both nitrogen and water vapor are with a range of 99.4% to 99.5% of the results of an ideal gas. Secondly, it can be notices that nitrogen and water vapor are within 99.9% of each other. These results are the same regardless of ambient temperature. We can conclude therefore that both water vapor and nitrogen approximate the properties of an ideal gas within the range of temperatures typically experienced by tires.

Note that this does NOT include the effects of condensation and the resultant loss of pressure.

[Chuck S.]

Re: Does Avagadro turn in his grave...

"...I'm not sure what Avagandro would think of this "new math", but he might damn it 6.023E23 times."

Hmmm...Appears to be a hint of sarcastic wit there...I think I'll take this window of opportunity to make the sophomoric declaration that:

"You can take the 'Boys' out of engineering, but you can NEVER take the engineering out of the 'Boys'!"

[Terry M.]

Does Avagadro turn in his grave...

I have marveled at this thread for two days now. It has brought me humor and wonderment at the knowledge of those participating on this board. I broke out in laughter (AIR.....it's a GAS) at work yesterday, and found myself trying to explain what was going on here to my colleagues -- some of them electrical engineers and an MBa -- in adjacent cubes. I eventually gave up -- they didn't see the humor -- maybe I'm warped.
Thanks to all of you for brightening the last couple of days.

[Duke W.]

OUTSTANDING POST!!!

It's nice to know we have a real scientist on the DB.

The dew point this morning was 9 deg. F, so I took the opportunity to change the air in the tires of my current daily driver that has to live in the driveway under a cover. It got down to 36 last night.

I won't have to worry about condensation, and your calculations clearly show that the difference between non-saturated air, and nitrogen are not measureable with common automotive tire gages.

Duke

[Dick W.]

Re: OUTSTANDING POST!!!

Dang!! I have gotten one heck of a migraine from tryin' to follow this post. Better'n goin' to college. Where are all the good lookin' co-eds??

[Chuck S.]

Re: OUTSTANDING POST!!!

Dickie, I'm trying to forget everything I learned in college...I only clicked on Jack's Avagadro post because I thought Avagadro was the guy that invented pizza.

[Rick S.]

Re: OUTSTANDING POST!!!

I thought Avagadro was the guy that had my back in 1966 at the POW camp. It must have been his brother delivering pizza.

[Dick S.]

Re: Questions about physics

I posted a response last night afte I got off the track, but I don't see it. I'll try to recreate it.

As I pointed out previously, superheated steam, occuring above the Pressure/Temperature (PT) boiling point, has zero relative humidity and is completely in the gasseous state. As such, it will react like an Ideal Gas. In a typical tire, we're interested in pressures somewhere between 20 psig (35 psia) to 40 psig (55 psia)and no greater than 210 F. This is well below the PT of boiling.

Lets look at the pressure cooker again. Lets remove all of the non water vapor and close the cooker. At 20 C (68 F) the pressure in the cooker is 17.5 mm Hg (.338 psia). If the vapor were reacting as an Ideal Gas and we double the temperature to 40 C (104 F) the pressure would be .676 psia, but according to the tables, it is 55.3 mm Hg or 1.069 psia. If we double the temperature again to 80 C (176 F), the pressure goes up to 355.1 mm Hg or 6.866 psia. Obviously not linear! This example is of course using saturated vapor pressure. Partial vapor pressure will be less, but also non linear.

[Duke W.]

Re: Questions about physics

And as I pointed out, water vapor in non-saturated air is superheated steam. Your pressure cooker example with the steam table data is about the vapor pressure of liquid water, which is a different problem that doesn't apply to water vapor in non-saturated air.

Mark Kozak ran the van del Waal equation calculations for water vapor and nitrogen and posted the results in his 1/6 11:40 PM post above.

His calculations answer the question about whether or not water vapor in non-saturated air behaves as an ideal gas or not to a reasonable approximation.

As I said before, if the temperature of the tire's contained air drops below the dew point and water condenses out, it's a different ball game, but if the temperature of your tire air doesn't fall below the dew point, then the difference in behavior of non-saturated air, dry nitrogen, and an ideal gas is within a fraction of a percent from zero to 100C - not enough to measure with usual tire pressure gages that most guys use.

So the conclusion is that dry nitrogen offers no benefit as long as your tire air is dry enough that it will not reach the dew point.

Duke

[Dick S.]

Re: Questions about physics

We're making a little more progress.

So your belief is that if there is 100% relative humidity (condensing)(saturated vapor pressure), the vapor pressure information I have been posting is valid and accurate and the pressure in the tire will change non-linearly with temperature but the instant the relative humidity drops below 100% (partial vapor pressure), it immediately becomes linear?

[Dick S.]

Re: Questions about physics

Hi Mark,

Does Van der Waals equation work under conditions of 100% relative humidity condensating?

How is the non-linearity of the vapor pressure of water explained with either the Ideal Gas law or Van Der Waals equation?