Talk:Density of air

Should this page be merged with Atmospheric pressure (or contrawise)?

Bot amok

The bot reverts the corrections someone else did to the formula - I just lost hours because the formula was wrong. Someone please correct this:

The pressure at altitude h is given by:

$p=p_{0}\cdot \left(1-{\frac {L\cdot h}{T_{0}}}\right)^{\frac {-g\cdot M}{R\cdot L}}$

to

The pressure at altitude h is given by:

$p=p_{0}\cdot 1000\cdot \left(1-{\frac {L\cdot h}{T_{0}}}\right)^{\frac {g\cdot M}{R\cdot L}}$

and

Density can then be calculated according to a molar form of the original formula:

$\rho ={\frac {p\cdot M}{R\cdot T}}\,$

where M is molar mass, R is the ideal gas constant, and T is absolute temperature.

to

Density can then be calculated according to a molar form of the original formula:

$\rho ={\frac {p}{R\cdot T}}\,$

R is the specific gas constant ( J/(kg*degK) = 287.05 for dry air), and T is temperature in deg K. — Preceding unsigned comment added by 94.222.121.251 (talk) 23:29, 7 November 2011 (UTC)

Duk 07:25, 28 Oct 2004 (UTC)

The right formula is

$p=p_{0}\cdot \left(1-{\frac {L\cdot h}{T_{0}}}\right)^{\frac {-g\cdot M}{R\cdot L}}$

The introduction of a constant factor like 1,000 arbitrarily, without including the units that would make it equivalent to the unit, 1, is incorrect. To show why this is so, let us look at a well-known formula for the distance d run at a constant speed v during a time period t:

d = v · t

This formula is right no matter what units you use for speed and for time, provided they are units of speed and of time, respectively. Now suppose you have been talking of metres per second and of seconds, so that the formula gives you distance in metres directly. But now you want to help the reader calculate the distance in inches. The right way to express that in the formula is

d = ( 1 in / 0.3048 m )· v · t

or

d = 3.28 in/m · v · t

but not

d = 3.28 · v · t

because the factor ( 1 in / 0.3048 m ) = 3.28 in/m is equivalent to 1, the unit, as one inch is equivalent to 0.3048 metres, and multiplying by 1 changes nothing. But the factor 3.28, without units, is clearly not equivalent to 1 and would change all. Kurt Artindagi (talk) 02:36, 30 November 2013 (UTC)

I suspect that they shouldn't be merged, because pressure and density are different concepts. As a quick example, please note that the density calculations require that local pressure be known. Alternately, pressure is an integration of density over altitude. However, the distinction may be more technical than useful, so if you would care to mention why you think there should be a merge, I may find myself enlightened.

Cheers, One-dimensional Tangent 00:36, 30 Oct 2004 (UTC)

Tangent, at first glance I thought these articles should be merged. Because in my mind I see the two concepts as mostly (but not completely) the same. But this is a mild opinion. The impetus was a desire to add information on various atmosphere models (MSIS, NRLMSISE ...) , but I wasn't sure were it should go. Maybe a dedicated page is better. Duk 01:45, 30 Oct 2004 (UTC)

Hmm... If you are planning on doing a page on the various models, or a page for each model, then the Density article would likely be redundant. In that case I definately see your point, and certainly have no objections.

The only thing I see in favor of keeping the Density article is that it might be simpler than MSIS-1986 and NRLMSIS-00, especially for people who only want a rough model and who don't need to know temperature, etc. However, all I know about atmospheric modelling is due to a few hours of light research, so I figure you're probably more qualified to judge this than I am.

So... I'll not take any offense at whatever you choose to do. -grin-

One-dimensional Tangent 02:40, 30 Oct 2004 (UTC)

The density formula had the wrong units, so I multiplied by M (to balance the mol and the Temperature) and divided by 1000 (for the gram to kilogram ratio). It now reads:

Density can then be calculated according to the original formula:

$\rho ={\frac {p\cdot M}{1000\cdot R\cdot T}}$

However, the external link http://wahiduddin.net/calc/density_altitude.htm also looks confused with its units, the gas constant starts off as

R = gas constant , J/(kg*degK) = 287.05

but later uses:

R = 8.31432 gas constant, J/ mol*deg K

This works out as the link uses M / 1000 to correct the different units, but this article appears to have forgotten them. -Wikibob | Talk 22:21, 2005 Jan 17 (UTC)

Since, in this article, you forgot to specify the units which you end up with, that 1000 is irrelevant.

Furthermore, make sure you specify which of the several units given will be used for the pressure (pascals, hectopascals, kilopascals), and check that kelvins per kilometre and see if that denominator fits in too. (Don't remember if units for height are specified in earlier formula, either—should be kilometres, I suppose, if you are using kelvins per kilometre. Gene Nygaard 22:32, 17 Jan 2005 (UTC)

Good point, I've removed the need for the 1000 by adjusting all the units except pressure to SI base units. This means pressure is in pascals, lapse rate in kelvin per metre (looks odd), and height in metres. Although standard units, the lapse rate, height and molecular weight may look odd to some, so here is an alternative with kilometres, and grams (this brings 1000 back, but that could be removed by using kPa for pressure.)

You should point out what mean air molecular mass you are using in the number of moles -- mass conversion.

---

Effects of altitude

To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere, using the universal gas constant instead of the specific one:

• sea level atmospheric pressure p₀ = 101325 Pa (= 101325 (kg/m·s²) = 1013.25 mbar or hPa = 101.325 kPa)
• sea level standard temperature T₀ = 288.15 K
• Earth-surface gravitational acceleration g = 9.80665 m/s².
• dry adiabatic lapse rate L = −6.5 K/km
• universal gas constant R = 8.31432 J/(mol·K)
• molecular weight of dry air M = 28.9644 g/mol

Temperature at altitude h kilometres above sea level is given by the following formula (only valid below the tropopause):

$T=T_{0}+L\cdot h$

The pressure at altitude h is given by:

$p=p_{0}\cdot (1+{\frac {L\cdot h}{T_{0}}})^{\frac {g\cdot M}{R\cdot -L}}$

Density can then be calculated according to a molar form of the original formula:

$\rho ={\frac {p\cdot M}{1000\cdot R\cdot T}}$

---

Finally for fun I've uploaded a javascript calculator that uses the above parameters here: http://www.geocities.com/robojojoba/air_density.html (source code in http://wikisource.org/wiki/Air_density_calculator) -Wikibob | Talk 00:24, 2005 Jan 22 (UTC)

In school i am designing a fictional planet that is completely water except for a few scattered volcanoes. Would the air be too dense for earth like animals to survive?

---

The text says:

molecular weight of dry air 28.9644 g/mol

the number is correct, and the unit is, but that MOLAR weight each mole of that element containing N (avogadro) molecules weight 28 grams or 0.028 Kg, that not the molecular weight but "molar weight" or "molal weight". Also naturally that mol means mole and not molecule, 28 g would be very heavy one :D

Awaiting international opinions before correcting (maybe international naming is different from my national one)

Gabriele Dini Ciacci 00:03, 13 November 2007 (UTC)

I agree. It should read "molar mass", and be linked to the appropriate wikipedia page. And 0.0289644 kg/mol should be restated as 28.9644 g/mol as you have above.Djd sd 06:13, 14 November 2007 (UTC)

Done. Djd sd 07:54, 16 November 2007 (UTC)

---

The link to the: eXtreme High Altitude Calculator is broken at today. if it keeps to be broken it needs to be removed

Gabriele Dini Ciacci 00:33, 13 November 2007 (UTC)

Let's take that whole line out. It does not really fit into the article. External links should be in the "External Links" section anyway.Djd sd 06:13, 14 November 2007 (UTC)

Done. Djd sd 07:54, 16 November 2007 (UTC)

Relative air density

\rho~_{_{humid~air}} = \frac{p_{d}}{R_{d} \cdot T} + \frac{p_{v}}{R_{v} \cdot T} —Preceding unsigned comment added by 134.221.122.71 (talk) 11:33, 17 February 2009 (UTC)

In my research on corona discharge, I find Peek's law (which I am writing). His book has a variable δ:

δ is the air density factor. It is calculated by the equation:

$\delta ={3.92b \over 273+t}$

where

• b = pressure in centimeters of mercury
• t = temperature in celsius

At SATP (25°C and 760 mmHg):

$\delta ={3.92\cdot 76 \over 273+25}=1$

I also come across this version of "relative air density":

$\delta ={b \over 101.3}{293 \over T}$

which looks at first glance to be the same thing with different units (kPa and K), but I am too tired to do the math. Then I find this formula which has several other variables:

RAD = Relative Air Density

BP = Barometric Pressure (inches??)

RH = Relative Humidity (percent)

T = Air Temperature (°F)

SP = Saturation Pressure (this value comes from a table included in the spreadsheet)

RAD = (1737.97 x (BP - (SP x RH/100))/(460 + T))

What is the relationship between these? Is one a standard formula that would be used in chemistry or whatever? Are b and T standard variable names for these quantities? Do the humidity values affect air density negligibly in most cases, so they are left out of the first ones? - Omegatron 02:54, August 8, 2005 (UTC)

Effects of temperature and pressure

Does anyone think the following line should be in slugs rather then lb_m?

• At standard ambient temperature and pressure (70 °F and 14.696 psia), dry air has a density of ρ_STP = 0.075 lb_m/ft³.

If we went to slugs, then the density would be around .00237 slugs/ft³ according to NASA

Regards Strefli3 21:23, 22 October 2006 (UTC)

There are many "standard" temperatures and pressures used. A user recently changed one of the given standards from 100 kPa to 1 Atm, but without any references or changes to the resulting value of air density. Since you can't change one without changing the other, I reverted the change. According to the linked "standard temperature and pressure" page, there are many standards. As the values listed on the page are just examples anyway, I feel the link to the appropriate Wikipedia page provides enough information to those looking for other standards. Maybe the most common should be listed, but they vary by country and industry. Otherwise we would have to list them all. Djd sd 16:04, 28 April 2007 (UTC)

Effect of water vapor

It seems that the following statement in the article is wrong: "pv = is also known as satuated preaure." Spelling mistakes aside, pv represents the partial pressure of water vapor. Saturation pressure and partial pressure should only be equal if relative humidity is 100%. I believe the correct relationship is pv=saturation pressure*relative humidity fraction. See http://wahiduddin.net/calc/density_altitude.htm as a reference. Djd sd 22:22, 19 March 2007 (UTC)

I made the change. I'll add references when I figure out how. I tried to make the section more clear, but it still needs a cleanup. Djd sd 06:50, 26 March 2007 (UTC)

You are correct about the saturated pressure. I have added the reference to the formula as well. Also in the first section, previously marked as confusing, the units were wrong, I fixed that. Generally it is my opinion that when the math is done using SI units, the result should be presented in those as well. . (Larkuur 09:34, 26 March 2007 (UTC))

Actually, it's not clear to me that units like slugs and pound-feet even belong in this article. Does anyone still learn physics in Imperial units? I realize that Americans still use sort-of-Imperial units in daily life, but I notice that car engines are specified in litres these days, not cubic inches; US scientists certainly use SI units, as does the country's military; and even drug dealers talk in grams and kilos. To me the old units seem useful for a pretty tiny number of readers, and a distraction for the large majority. Oxymetheus —Preceding unsigned comment added by 65.38.32.131 (talk) 00:00, 1 April 2009 (UTC)

Need more real-world data points

This article needs more real-world data points. It is fine to be told the density of "dry air", but many readers are likely to want to know the density of the actual air around them -- so, please give some actual densities, at typical humidity, temp, elevation, pressure, etc. -69.87.199.142 23:48, 23 August 2007 (UTC) Agree with comment above. Something practical might be, how much does the air in my lungs shrink when I go down to the bottom of a 12' deep pool. Or, at what depth of water does a one gallon plastic jug of air become a half gallon? JCW 108.23.6.178 (talk) 05:18, 12 September 2013 (UTC)

Standard temperature and pressure

Let's stay consistent with the standard temperature and pressure values. Every so often these data points are changed, sometimes incorrectly. I just looked up the International Standard Atmosphere (as referenced in the "Effects of altitude" section), sea level pressure is 101325 Pa, and sea level temperature is 15° C (288.15 K). There are references to other standards in the "Effects of temperature and pressure" section. We should probably standardize those, too. Or we should at least provide references as to which standards are being used so that the values can be verified. Djd sd 11:40, 30 October 2007 (UTC)

Implementing the formula

I don't know if my understanding is wrong or if the article is not clear enough but to get the "density of dry air calculated using the ideal gas law" formula to work I had to make a some changes. I see that other people in this discussion page have also done similar things ie. multiplying by 1000 etc. I probably didn't read/think about the formula enough, but perhaps a worked through example would help instead of just the formula and the result.

To get this to work:

p = p / (R * T)

for: "At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m3"

ie. 20 °C, 101.325 kPa and 287.05 J/(kg·K) do not just slot straight in to the above formula to get 1.2041. I convert °C to Kelvins and I also multiply by 1000. I think I am multiplying to 1000 to get Pa as opposed to kPa so I have thrown it in with the p component, however it is entirely possible this incorrect.

C/C++/Javaish/Javascriptish:

float DegreesCelciusToKelvin(float fDegreesCelcius) { return fDegreesCelcius + 273.15f; }

float GetDensityOfAirKgPerCubicMeterForPressureKPAAndTemperatureDegreesCelcius(float fPressureKPA, float fTemperatureDegreesCelcius)
{
  const float p = 1000.0f * fPressureKPA; // absolute pressure must be in Pa not KPA
  const float R = 287.05f; // specific gas constant for dry air is 287.05 J/(kg·K) in SI units
  const float T = DegreesCelciusToKelvin(fTemperatureDegreesCelcius); // absolute temperature

  return (p / (R * T));
}

Hullo exclamation mark (talk) 21:11, 9 October 2009 (UTC)

ISA density for aeronautics?

I came to this page looking to confirm the ISA air density (1.225 kg/m3) but couldn't find it. I see this figure for the ISA temperature of 15 deg C but this requires remembering ISA conditions. Would be handy to have some aeronautics-related info if anyone has the time to put it in. Good reference is atmosphere chapter of Shevell's Fundamentals of Flight. Cheers 203.129.23.146 (talk) 22:15, 7 May 2011 (UTC)

Why are properties of sound in dry air mentioned?

Properties of sound are interesting but I see no reason why are they mentioned in the table that should show the density of air. I suppose the extra columns could be moved elsewhere. Simbulu (talk) 23:04, 22 October 2011 (UTC)

g/cc

I can't think of ANY good reason why air's density in g/cc isn't provided here. A large fraction of the human race uses this as the common units for density. Its absence is embarrassing. I'm adding it.Abitslow (talk) 13:11, 12 November 2013 (UTC)