# Is air density a state function?

• TonyG
In summary: State or path? If you know the difference, you know the answer to your question. Is this a "troll" of some sort?
TonyG
I know there is a simple equation using absolute pressure and absolute temperature that predicts the density air in our atmosphere. This is commonly used in weather forcasting.

My question is that if air undergoes a process of compression, cooling, etc...ending up at a pressure P and a temperature T, will it's density be the same as "atmospheric air" at (P,T) predicted by the equation mentioned above?

which equation?

The ideal gas equation essentially. There are numerous "air density calculators" at weather-related websites. Some of the more sophisticated calculators have correction terms for humidity and altitude. Just do a google search on "air density calculator" and you'll find a lot of them. So returning to my original question, is air density is a state function or a path function?

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Originally posted by TonyG
(snip)So returning to my original question, is air density is a state function or a path function?

"State or path?" If you know the difference, you know the answer to your question. Is this a "troll" of some sort?

It is a state function.

Originally posted by Bystander
"State or path?" If you know the difference, you know the answer to your question. Is this a "troll" of some sort?

No, just a physicist who's been working in industry and became a little "out of touch" with basic thermodynamics. Intuitively, I was sure it depended on P and T, not how it got there, but in the heat of a discussion with someone on the topic, I became a little uncertain and needed a sanity check. No need to flame, I'm new on this forum.

Welcome to the forums!

I hope you will stick around, we appreciate knowledgeable contributors. Browse around, I think you will find we are generally a pretty friendly group, but have a low tolerance for crackpots.

Originally posted by TonyG
No, just a physicist who's been working in industry and became a little "out of touch" with basic thermodynamics. Intuitively, I was sure it depended on P and T, not how it got there, but in the heat of a discussion with someone on the topic, I became a little uncertain and needed a sanity check. No need to flame, I'm new on this forum.

Not a flame --- just a thermodynamicist who's a bit out of touch with degree programs that handle thermo as a "throwaway" course. Where is the emphasis placed these days? QM? Solid state? Quarks? Strings?

And what sort of credentials were you arguing against? A Chem. E., perhaps?

Originally posted by Bystander
Not a flame --- just a thermodynamicist who's a bit out of touch with degree programs that handle thermo as a "throwaway" course. Where is the emphasis placed these days? QM? Solid state? Quarks? Strings?
How important thermo is (and how it is approached) depends a lot on what major we're talking about of course. It was pretty important in my mechanical engineering program. But strictly macroscopic: thermo cycles and heat transfer.

For my Physics BS I did a year of Statistaical Thermodynamics from Kittels book. I learned that fundamental Thermodynamic is very difficult and really did not learn anything as useful as Russ did from his Macroscopic view point. I do have a gut level understanding of what is happening physically, but could not but it to formal use.

Russ, Integral-

Thanks for the comments. TonyG, I'm not deliberately hijacking your thread --- you have been reassured that density is a state function, which was your initial question. It does bring up the question of "What is missing in the thermo courses for physics majors; there is a striking lack of confidence in the basic concepts of thermo as demonstrated by the credentialled physicists in the PF forums." Integral furnishes a clue in the remark that thermo comes from Kittel (not a bad book, but totally inappropriate for teaching/learning thermo). The statistical-(mechanical/physical/thermodynamic) short cut taken in developing the concepts leaves enormous holes in actual understanding of the field.

Is this even close to a reasonable assessment of what happens: "Thermo is a foundation of physics, therefore all physics majors must hear the word at least once in their coursework, but it ain't sexy, we, the faculty, don't know any thermo, so we'll use a "consensus" text and require junior faculty to handle the course as part of their teaching load"?

There is no great demand for thermodynamicists, but am I out of line in my expectations of a minimum exposure to principles and development of confidence in the applications of those principles?

Originally posted by Integral
...did not learn anything as useful as Russ did from his Macroscopic view point.
Engineering Thermo is a rarity - the intro course is a mixture of theory and application that is very practical and highly useful. From there you get into heat transfer and far more theoretical (and less useful for an undergrad) courses for the most part. Most other engineering courses are the opposite - heavy theory in the beginning leading to useful application 2 courses later.

Your comment about Kittel makes me feel a bit better. I had a very hard time connecting Kittels development to the real world. This real world connetion is necessary for me to grasp the topic.

Naturally, the quality of the course depends a lot on the prof, but I think, at least my University, made a decent effort to present the material.

In retrospect, (it has been nearly 30yrs since I took the course) Thermo may have been a single term and not a full year. This would definatly make it the poor step sister of the major courses, Quantum, E&M, Mechanics etc.

Originally posted by Bystander
you have been reassured that density is a state function, which was your initial question.

Yes, thanks. I just have some bizarre compressor/intercooler data that I'm trying to understand.

I was kind of looking for some type of an effect where the water content of the air is affected by the compression process. I've been told that compressing air reduces its ability to hold water in the vapor state, but I'm not too sure about that. If it's true, then its not inconceiveable that air density at some specific pressure and temperature is sensitive to the process it has undergone (but I'm haven't really thought that over yet).

Thanks anyway for all your help.

Water in air? Welcome to the wonderful world of non-reactive "pseudo" two component systems; your first approximation is to ignore the air entirely, and look only at the partial density (or partial pressure) of the water vapor --- once it reaches the dew point density (or vapor pressure) for the temperature you're operating at, it condenses. The system isn't ideal, meaning there are odd corrections, but this gets you into the 10% ballpark.

Also, see "phase separation" in whatever you've got handy for thermo references.

Originally posted by TonyG
Yes, thanks. I just have some bizarre compressor/intercooler data that I'm trying to understand.

I was kind of looking for some type of an effect where the water content of the air is affected by the compression process. I've been told that compressing air reduces its ability to hold water in the vapor state, but I'm not too sure about that. If it's true, then its not inconceiveable that air density at some specific pressure and temperature is sensitive to the process it has undergone (but I'm haven't really thought that over yet).
Thanks anyway for all your help.

Took Chemistry in University, it's true, compressing air reduces it's saturation point, and in the compression process it generally releases some of the water vapor that it had from atmospheric conditions.

I suspect what you are loking for is STP (Standard Temperature and Pressure) which is the established benchmark.

If you still uncertian about the air, go to any car service station and ask them if they have problems with the water producd by there compressor, especially in auto "air spray painting", water separators are expensive. (I know!)

## 1. What is a state function?

A state function is a physical property that is independent of the path taken to reach a particular state. It only depends on the current state of the system and not on how the system got there. Examples of state functions include temperature, pressure, and energy.

## 2. Is air density a state function?

Yes, air density is a state function. It only depends on the current state of the air, such as temperature and pressure, and does not depend on the process that led to that state.

## 3. How is air density calculated?

Air density is calculated using the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume. It is also affected by the type of gas and its molecular weight.

## 4. Does air density change with altitude?

Yes, air density does change with altitude. As altitude increases, the air pressure and temperature decrease, which leads to a decrease in air density. This is why it is harder to breathe at high altitudes.

## 5. How does air density affect the flight of airplanes?

Air density plays a crucial role in the flight of airplanes. As air density decreases with altitude, the lift force on the wings also decreases, making it harder for the airplane to stay in the air. This is why airplanes need to adjust their speed and angle of attack as they change altitude.

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