Confused by temperature's effects on air pressure

[SpiffyPhysics]

Hi,
I'm an instructor at an online school, and my text says
“ Air pressure is the amount of pressure the atmosphere places on the surface of Earth. Air pressure is usually measured as the weight of the column of air above a square meter (N/m2). As altitude increases, air density decreases and so does air pressure. Air pressure is also impacted by temperature. As temperature increases, the air pressure increases. Cooler air has lower air pressure.”

And I got the following question from a colleague "Isn’t this backwards? The above is true in a sealed container, but not in the atmosphere."

And I am really having trouble finding the right answer; almost everything I can find says that pressure and temperature are directly related, but I fear that they are referring to gas in a closed container but not specifying that.
And anything I can find about the atmosphere gets confusing; some sources say there is a direct relationship, some say that when temperature rises the air becomes less dense and the pressure decreases, one says that temperature and pressure rise together and fall together and then in the next paragraph it says "Very cold temperatures can create areas of high air pressure because cold air has greater density and the concentration of molecules can raise the air pressure."

So can someone clear this up for me? When air is in the atmosphere instead of in a closed container, what happens to the air pressure as the temperature increases?


Thank you in advance!

 

[Chestermiller]

Hi,
I'm an instructor at an online school, and my text says
“ Air pressure is the amount of pressure the atmosphere places on the surface of Earth. Air pressure is usually measured as the weight of the column of air above a square meter (N/m2). As altitude increases, air density decreases and so does air pressure. Air pressure is also impacted by temperature. As temperature increases, the air pressure increases. Cooler air has lower air pressure.”

And I got the following question from a colleague "Isn’t this backwards? The above is true in a sealed container, but not in the atmosphere."

And I am really having trouble finding the right answer; almost everything I can find says that pressure and temperature are directly related, but I fear that they are referring to gas in a closed container but not specifying that.
And anything I can find about the atmosphere gets confusing; some sources say there is a direct relationship, some say that when temperature rises the air becomes less dense and the pressure decreases, one says that temperature and pressure rise together and fall together and then in the next paragraph it says "Very cold temperatures can create areas of high air pressure because cold air has greater density and the concentration of molecules can raise the air pressure."

So can someone clear this up for me? When air is in the atmosphere instead of in a closed container, what happens to the air pressure as the temperature increases?


Thank you in advance!

The temperature of the air varies substantially with altitude, and the entire temperature profile above a given altitude affects the pressure at that altitude. Are you comfortable with mathematics, including integral calculus?

 

[sophiecentaur]

And I got the following question from a colleague "Isn’t this backwards? The above is true in a sealed container, but not in the atmosphere."

To understand what goes on in the atmosphere, one must first remember and understand the basic laws that apply to gases in 'small' quantities. This is only a part of the reason for what happens in the atmosphere, which is very complicated and it is not static. Sunlight warms up the Earth's surface, some of the energy in sunlight is absorbed in the air on the way down and also the infrared radiation from the warm surface is absorbed by the air. The pressure at any height is largely caused by the 'weight' of the air above.
PF has frequent exchanges about what really goes on up there and members have varied knowledge and opinions. Discussions can be quite heated. Any complete model has to include all the above factors (and more), which is why I say it's essential to know the basic gas laws off by heart - and believe that they have to apply up there. If they are apparently not working it must be because of something at work that you haven't thought of.

 

[Bystander]

quite heated.

+1

 

[sophiecentaur]

+1

That issue ranks a close second to what generates lift on a wink. (I mistyped the k but I will leave it)

 

[Chestermiller]

@SpiffyPhysics How are you at math (including calculus)? If you like, I will show the detailed development for the global average pressure profile, assuming aerostatic equilibrium. Any interest in seeing it?

 

[SpiffyPhysics]

@SpiffyPhysics How are you at math (including calculus)? If you like, I will show the detailed development for the global average pressure profile, assuming aerostatic equilibrium. Any interest in seeing it?

Thank you but no thank you...I've been teaching high school too long and left all of my understanding of calculus behind somewhere.

Is there a simplified version to consider? (This is actually for a 9th grade Earth science course, and it's online in an environment that doesn't allow for class discussion) If we don't consider the big complicated atmosphere but just a small quantity of gas that isn't in a closed container, does an increase in temperature increase the pressure? Or is there no way to give a simplified general answer?

 

[SpiffyPhysics]

To understand what goes on in the atmosphere, one must first remember and understand the basic laws that apply to gases in 'small' quantities. This is only a part of the reason for what happens in the atmosphere, which is very complicated and it is not static. Sunlight warms up the Earth's surface, some of the energy in sunlight is absorbed in the air on the way down and also the infrared radiation from the warm surface is absorbed by the air. The pressure at any height is largely caused by the 'weight' of the air above.
PF has frequent exchanges about what really goes on up there and members have varied knowledge and opinions. Discussions can be quite heated. Any complete model has to include all the above factors (and more), which is why I say it's essential to know the basic gas laws off by heart - and believe that they have to apply up there. If they are apparently not working it must be because of something at work that you haven't thought of.

I was afraid of that. Is there a simplified version to consider? (This is actually for a 9th grade Earth science course, and it's online in an environment that doesn't allow for class discussion) If we don't consider the big complicated atmosphere but just a small quantity of gas that isn't in a closed container, does an increase in temperature increase the pressure?

 

[jbriggs444]

I was afraid of that. Is there a simplified version to consider? (This is actually for a 9th grade Earth science course, and it's online in an environment that doesn't allow for class discussion) If we don't consider the big complicated atmosphere but just a small quantity of gas that isn't in a closed container, does an increase in temperature increase the pressure?

If you are dealing with a gas in an open container exposed to the rest of the room then the pressure in the gas is the same as the pressure in the room (*). That's Pascal's principle.

(*) This holds as long as the density of the air times the height of the room is negligible for your measurement precision, that you are not counting noises as pressure variations and you do not have any significant winds.

 

[Chestermiller]

Thank you but no thank you...I've been teaching high school too long and left all of my understanding of calculus behind somewhere.

Is there a simplified version to consider? (This is actually for a 9th grade Earth science course, and it's online in an environment that doesn't allow for class discussion) If we don't consider the big complicated atmosphere but just a small quantity of gas that isn't in a closed container, does an increase in temperature increase the pressure? Or is there no way to give a simplified general answer?

If it's open to the atmosphere at ground level, then the pressure is atmospheric pressure.

 

[OldYat47]

Keeping it as simple as possible, if we assume that the temperature gradient of a column of air over a particular area gets uniformly warmer (say, +5 deg. at each temperature level) then the atmospheric pressure will decrease. I think your source has a typo.
Interestingly (and not related directly to your question), air that is more humid is lighter than air that is dryer. For those of us who live in hot, humid areas this is counter intuitive because hot, humid air feels subjectively heavy.

 

[SpiffyPhysics]

Thank you for your help everyone!