(air) density and molecules
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(air) density and molecules
If a substance is heated or cooled, do the molecules expand or contract to any degree? If so does that contribute significantly to the overall density of the material?
Or is the density related more to the increased/decreased motion of the molecules, and therefore the collisions between them, therefore taking more/less space?
If it makes any difference, I'm interested in air density in particular.
Mike
Or is the density related more to the increased/decreased motion of the molecules, and therefore the collisions between them, therefore taking more/less space?
If it makes any difference, I'm interested in air density in particular.
Mike
Last edited by mstram; 14th Jul 2004 at 23:28.
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mstram,
as air is heated, the average kinetic energy of the molecules increases, thus allowing each molecule to occupy a greater volume in space. Same mass, greater volume = lower density.
In the atmosphere (or any fluid under the effect of a constant force in one direction, ie. Gravity) the denser fluid will sink to the bottom of the "container" thus PUSHING UP the less dense fluid.
So yes, when you see a thunderstorm, or even a cumulus cloud, its the colder air that sinks on the edges of the storm that pushes up the warm, less dense air in the cloud.
If on the other hand you are talking about a fluid in an enclosed container, an increase in temperature will lead to an increase in pressure, but no change in density since the overall mass (# of molecules) in the enclosed volume do not change. However, the added kinetic energy allows them to push harder onto the sides of the container, increasing the pressure.
Hope this makes sense,
palgia
as air is heated, the average kinetic energy of the molecules increases, thus allowing each molecule to occupy a greater volume in space. Same mass, greater volume = lower density.
In the atmosphere (or any fluid under the effect of a constant force in one direction, ie. Gravity) the denser fluid will sink to the bottom of the "container" thus PUSHING UP the less dense fluid.
So yes, when you see a thunderstorm, or even a cumulus cloud, its the colder air that sinks on the edges of the storm that pushes up the warm, less dense air in the cloud.
If on the other hand you are talking about a fluid in an enclosed container, an increase in temperature will lead to an increase in pressure, but no change in density since the overall mass (# of molecules) in the enclosed volume do not change. However, the added kinetic energy allows them to push harder onto the sides of the container, increasing the pressure.
Hope this makes sense,
palgia
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palgia,
thx for the explanation.
I've read about molecules speeding up / kinetic energy increasing, but haven't seen anything about molecules changing size. (Maybe because it never happens ?
).
Mike
thx for the explanation.
I've read about molecules speeding up / kinetic energy increasing, but haven't seen anything about molecules changing size. (Maybe because it never happens ?
).Mike
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Hello,
The definition of temperature is such that it can be thought of as a direct measure of the level of molecular motion (a simplification) i.e. hot objects contain molecules that exhibit more motion than those in a cooler object (in general...again, a valid simplification). Think of molecular motion as vibrational and translational i.e. each molecules vibrates as it moves (translates) around.
The density of a gas is simply the mass per unit volume, which is affected by temperature. A higher temperature means more molecular motion (by definition). More molecular motion means, when they hit things, the molecule's impart more force which in turn means the pressure exerted by the gas increases - this causes the gas to exert more force on the walls of its container and, assuming it has enoughy give, cause the container (and therefore the volume occupied by the gas) to expand. Same mass in a bigger volume means lower density.
As density is just mass per unit volume you can see that if you imagine a certain number of gas molecules then it is the distance between them in a certain region which determines the density i.e. if they're far apart then there'll be less in a given volume therefire there'll be less mass in a given volume i.e. the density is lower.
Even if the individual molecules expanded by any appreciable degree (which they don't really) e.g. they doubled in size, you can picture how this would have no real impact on the density: there would still be more or less the same number in a given volume (say 1m^3), they'd just be a "stretched" a bit more - you can see this by just sketching a box with some molecules in then strecthing each one - the number of molecules is, for all intents and purposes, the same. This means the mass in the volume is unchanged which means the density is unaffected.
Thus it's the temperature (= molecular motion) of the substance that affects density, not any expansion/contraction of the individual molecules (which is practically non-existent anyway).
Hope this helps,
V1R
The definition of temperature is such that it can be thought of as a direct measure of the level of molecular motion (a simplification) i.e. hot objects contain molecules that exhibit more motion than those in a cooler object (in general...again, a valid simplification). Think of molecular motion as vibrational and translational i.e. each molecules vibrates as it moves (translates) around.
The density of a gas is simply the mass per unit volume, which is affected by temperature. A higher temperature means more molecular motion (by definition). More molecular motion means, when they hit things, the molecule's impart more force which in turn means the pressure exerted by the gas increases - this causes the gas to exert more force on the walls of its container and, assuming it has enoughy give, cause the container (and therefore the volume occupied by the gas) to expand. Same mass in a bigger volume means lower density.
As density is just mass per unit volume you can see that if you imagine a certain number of gas molecules then it is the distance between them in a certain region which determines the density i.e. if they're far apart then there'll be less in a given volume therefire there'll be less mass in a given volume i.e. the density is lower.
Even if the individual molecules expanded by any appreciable degree (which they don't really) e.g. they doubled in size, you can picture how this would have no real impact on the density: there would still be more or less the same number in a given volume (say 1m^3), they'd just be a "stretched" a bit more - you can see this by just sketching a box with some molecules in then strecthing each one - the number of molecules is, for all intents and purposes, the same. This means the mass in the volume is unchanged which means the density is unaffected.
Thus it's the temperature (= molecular motion) of the substance that affects density, not any expansion/contraction of the individual molecules (which is practically non-existent anyway).
Hope this helps,
V1R
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Not a simple question and one which probably needs the physicist people to offer comment. 'Size' of molecules and atoms (which, I might add, is out of my routine ambit) is a bit rubbery due to the notion of electrons having both mass and wave properties. Probably, at the air temperatures for which you most likely are interested, such notions won't be significant.
The following paper might give you some food for thought .. albeit at the expense of needing to skip over a few of the sums ....
The following paper might give you some food for thought .. albeit at the expense of needing to skip over a few of the sums ....
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We probably need a chemist or physicist to answer that.
But since I'm at it, I'll give ity a shot
When you say "change in size" do you mean an increase in the volume they occupy in space?
Or do you mean an increase in mass (ie. a chemical reaction that would add more atoms to that molecule) ?
If you mean the volume then yes, it would increase in volume for the reasons listed above (and maybe other reasons unknown to me
).
If you mean increase in mass, I believe you need either a chemical reaction or a means to accelerate the mass in question to a VERY fast speed (the closer to the speed of light, the better).
Don't think I can contribute at any higher level, chemistry in not my thing.
palgia
PS. Just out of curiosity, are you asking out of personal interest or are you trying to apply this to some practical application (ie. answer the ATPL MET questions) ?
But since I'm at it, I'll give ity a shot
When you say "change in size" do you mean an increase in the volume they occupy in space?
Or do you mean an increase in mass (ie. a chemical reaction that would add more atoms to that molecule) ?
If you mean the volume then yes, it would increase in volume for the reasons listed above (and maybe other reasons unknown to me
).If you mean increase in mass, I believe you need either a chemical reaction or a means to accelerate the mass in question to a VERY fast speed (the closer to the speed of light, the better).
Don't think I can contribute at any higher level, chemistry in not my thing.
palgia
PS. Just out of curiosity, are you asking out of personal interest or are you trying to apply this to some practical application (ie. answer the ATPL MET questions) ?
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I've just (somehow) graduated with a physics degree - if you need any more detail than what's above, I could try and help some more.
Cheers,
V1R
Cheers,
V1R
Couple a numbers for you. You get avogadro's number of gas molecules in the standard molar volume. That's 6 x 10^23 molecules per 22.4 litres (2.24x 10^-2 m^3).
So the volume per molecule is 2.24x 10^-2 m^3/ 6 x 10^23 or about 3 x 10^-26 m^3. If you divide that up per molecule, it's about a 30 angstrom sided cube.
A nitrogen molecule has a bond length of about an angstrom.
So it really doesn't make much difference if the bond stretches a bit. In fact, it doesn't make much difference what length the bond is at all! -- the molecular volume of gases is the same, as their molecular speed distribution only really depends on the temperature.
So the volume per molecule is 2.24x 10^-2 m^3/ 6 x 10^23 or about 3 x 10^-26 m^3. If you divide that up per molecule, it's about a 30 angstrom sided cube.
A nitrogen molecule has a bond length of about an angstrom.
So it really doesn't make much difference if the bond stretches a bit. In fact, it doesn't make much difference what length the bond is at all! -- the molecular volume of gases is the same, as their molecular speed distribution only really depends on the temperature.
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>PS. Just out of curiosity, are you asking out of personal interest or are you trying to apply this to some practical application (ie. answer the ATPL MET questions)
Palgia :
Just personal interest. Hopefully I haven't given the authorities any ideas for an even dumber test question than usual. (Even though I'm in Canada, it seems like all aviation tests around the world are designed in the same obscure way
)
V1 - thx, I think I'll just accept the fact that molecules (usually) don't change size. Getting into the details tends to be incomprehensible anyway
BW: Thx for the info
Mike
Palgia :
Just personal interest. Hopefully I haven't given the authorities any ideas for an even dumber test question than usual. (Even though I'm in Canada, it seems like all aviation tests around the world are designed in the same obscure way
)V1 - thx, I think I'll just accept the fact that molecules (usually) don't change size. Getting into the details tends to be incomprehensible anyway
BW: Thx for the info
Mike
Yes, the size change for a molecule is virtually non-existent relative to the space it (the molecule) has to bounce around in in air. Short of tossing a molecule into the sun, where it might fragment, you won't see enough change to make a difference to anything that would concern a pilot.
However, the density of air has a lot to do with lift generated over an airplane wing, and altitude affects that. (Higher altitude = less air = lower density)
Also, temperature does affect the density altitude. When it is hot, there are fewer molecules in a given volume of space, so the density is lower, and you get less lift.
Humidity affects density altitude too, as water molecules weigh less than nitrogen or oxygen molecules, so provide less lift. (Never checked on the physics of that however.)
However, the density of air has a lot to do with lift generated over an airplane wing, and altitude affects that. (Higher altitude = less air = lower density)
Also, temperature does affect the density altitude. When it is hot, there are fewer molecules in a given volume of space, so the density is lower, and you get less lift.
Humidity affects density altitude too, as water molecules weigh less than nitrogen or oxygen molecules, so provide less lift. (Never checked on the physics of that however.)
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visibility3miles
Yes indeed, but remember that the maximum amount of water vapour strongly depends on the temperature :
The maximum mass fraction of water in saturated air is below 5%, in which case the density of the mixture will only be 2% less than the density of dry air in the same conditions. This figure will drop to 0.5% at 20 deg C.
No big influence on aircraft performance at ground level (and nothing at all at high altitude)
Humidity affects density [altitude?] too, as water molecules weigh less than nitrogen or oxygen molecules
The maximum mass fraction of water in saturated air is below 5%, in which case the density of the mixture will only be 2% less than the density of dry air in the same conditions. This figure will drop to 0.5% at 20 deg C.
No big influence on aircraft performance at ground level (and nothing at all at high altitude)
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If a substance is heated or cooled, do the molecules expand or contract
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Bre 901,
I agree that the effect is not enormous, but I don't think its negligeble either. (and neither does the FAA, which dedicated an entire issue of the Aviation Safety magazine a couple of months ago to illustrate the effect of moisture on density altitude).
I did some number crunching and came up with values very similar to your's: about a 1.9 - 2.4% reduction in density.
This might not seem much, but to but it into perspective, on a hot day (35C) it is equivalent to the density reduction created by an additional 8degrees C. In other words, on a very humid day, when the reported temperature is 35C, your aircraft is performing as if the temperature was 43C.
On the aircraft I fly (normally aspirated high performance light twin) this translates into a 13% increase in Takeoff distance, as well as a 25% loss in single engine climb performance (well, not sure we can talk of single engine climb performance on light twins
) or in other words the same performance loss due to a 25% increase in payload.
Now, I do agree that the above example is more of an extreme situation (35C with 85%RH), and that more realistically, we are talking about a "density penalty" equivalent to a 5-6C temperature increase. Furthermore I understand that in many areas of the world this spread is further reduced since the temperatures never get this high. But in tropical areas (where I fly), as well as other climates during the summer months, humidity DOES affect take-off performanve in a non-trivial way.
This can be noticed by seeing an increased deviation between the performance numbers in the POH/AFM and the actual performance you get in the aircraft (as opposed to a lesser difference under cooler and dryer conditions).
Although I've never flown jets, I would imagine that under certain conditions, large amounts of water vapour could affect performance. (I am thinking about some central/south american airports at high elevations, high temperatures, just a couple of hours following a brief-but-intense afternoon shower, high TEMP/RH combination, not so long rwy, don't you think that the "density penalty" due to moisture of about 5C would cause a non-trivial hit on the rwy limited TO weight? I would think so, and probably that's why the airlines don't want to know about it
)
I took a dispatching course but was never taught to incorporate humidity in the performance calculation. Does anyone know if any airlines do consider humidity?
I know that the ops specs list the rwy limited weight in a tabulated format that has temperature in one degree celsius increments. That means that the engineers are concerned with up to one degree accuracy in the field temperature but do not even consider humidity
palgia
PS. Correct me if i'm wrong, but the standard atmosphere engineers use is 21% oxy, 78% nitrogen and a few other gasses. No moisture? Are they calculating nubers for DRY AIR?
I agree that the effect is not enormous, but I don't think its negligeble either. (and neither does the FAA, which dedicated an entire issue of the Aviation Safety magazine a couple of months ago to illustrate the effect of moisture on density altitude).
I did some number crunching and came up with values very similar to your's: about a 1.9 - 2.4% reduction in density.
This might not seem much, but to but it into perspective, on a hot day (35C) it is equivalent to the density reduction created by an additional 8degrees C. In other words, on a very humid day, when the reported temperature is 35C, your aircraft is performing as if the temperature was 43C.
On the aircraft I fly (normally aspirated high performance light twin) this translates into a 13% increase in Takeoff distance, as well as a 25% loss in single engine climb performance (well, not sure we can talk of single engine climb performance on light twins
) or in other words the same performance loss due to a 25% increase in payload. Now, I do agree that the above example is more of an extreme situation (35C with 85%RH), and that more realistically, we are talking about a "density penalty" equivalent to a 5-6C temperature increase. Furthermore I understand that in many areas of the world this spread is further reduced since the temperatures never get this high. But in tropical areas (where I fly), as well as other climates during the summer months, humidity DOES affect take-off performanve in a non-trivial way.
This can be noticed by seeing an increased deviation between the performance numbers in the POH/AFM and the actual performance you get in the aircraft (as opposed to a lesser difference under cooler and dryer conditions).
Although I've never flown jets, I would imagine that under certain conditions, large amounts of water vapour could affect performance. (I am thinking about some central/south american airports at high elevations, high temperatures, just a couple of hours following a brief-but-intense afternoon shower, high TEMP/RH combination, not so long rwy, don't you think that the "density penalty" due to moisture of about 5C would cause a non-trivial hit on the rwy limited TO weight? I would think so, and probably that's why the airlines don't want to know about it
)I took a dispatching course but was never taught to incorporate humidity in the performance calculation. Does anyone know if any airlines do consider humidity?
I know that the ops specs list the rwy limited weight in a tabulated format that has temperature in one degree celsius increments. That means that the engineers are concerned with up to one degree accuracy in the field temperature but do not even consider humidity
palgia
PS. Correct me if i'm wrong, but the standard atmosphere engineers use is 21% oxy, 78% nitrogen and a few other gasses. No moisture? Are they calculating nubers for DRY AIR?
Good comments palgia.
My understanding, after a bit of digging, is that the standard atmosphere is defined using the hyrdostatic constant
g * Mm / R = 34.163 K/km
That would make the molar mass Mm = 28.95 g/mol
I believe that is dry air (approx 78% N2, 21% O2, 1% Ar).
PS. Correct me if i'm wrong, but the standard atmosphere engineers use is 21% oxy, 78% nitrogen and a few other gasses. No moisture? Are they calculating numbers for DRY AIR?
g * Mm / R = 34.163 K/km
That would make the molar mass Mm = 28.95 g/mol
I believe that is dry air (approx 78% N2, 21% O2, 1% Ar).
Last edited by bookworm; 16th Jul 2004 at 08:44.
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humidity is important
Yes palgia and others. If you take my base airport at 317 ft AMSL, 15deg C air temp and 10deg C dew point the density altitude is 550ft when the baro reads 1013mb. Now the glass falls to 1000mb. What’s 13mb? Well in consequence the density altitude jumps up to 1000ft… nearly doubles. Suppose barometer and dew point stay the same at 1000mb and 10deg C but the day hots up. What happens? Well the relative humidity falls for one thing. At 20deg C the relative humidity has fallen from 72% to 53% and the density altitude is now 1583ft … more than 1000ft higher than the chart. Temperature goes on rising everything else remains constant but the day hots up to 25deg C… now the relative humidity is 39%, much more pleasant under the armpits but the density altitude is 2153ft which is 1800ft more than the chart! Finally for the sake of argument the day tops off at 30deg C still with baro and dew point stuck at 1000mb and 10 deg C. What’s the relative humidity and density altitude now? Answer 29% and 2712ft. Now from beginning to end of this example the relative density of the air has only changed by 5% - it was 97% first thing and is now 92%. But it feels so fresh now from the cool and damp in the morning. I’m not going to have lift and icing problems am I?
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nigel just remembered
the man to my right has just kindly reminded me that if your computer does not have an input for relative humidity or dew point it defaults to believing that at 43 deg C the rel humidity is 34% and at 15 deg C it believes rel humidity is 80% with a linear variation between these values which are treated as end-stops. i do remember it come to think of that and if you play with richard shelquist's lovely on-line density altitude calculators (he calls himself "wahiduddin" you'll see what merry heck gross errors make on your take-off performance. doncha just hate it when the man in the right seat is smarter than you?
