# Confused by temperature's effects on air pressure

• SpiffyPhysics
In summary, pressure and temperature are directly related in closed containers, but not in the atmosphere.
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!

SpiffyPhysics said:
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?

SpiffyPhysics said:
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.

sophiecentaur said:
quite heated.
+1

sophiecentaur
Bystander said:
+1
That issue ranks a close second to what generates lift on a wink. (I mistyped the k but I will leave it)

@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?

Chestermiller said:
@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?

sophiecentaur said:
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?

SpiffyPhysics said:
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.

SpiffyPhysics said:
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.

jbriggs444
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.

Thank you for your help everyone!

## What is the relationship between temperature and air pressure?

The relationship between temperature and air pressure is known as the Ideal Gas Law, which states that as temperature increases, air molecules have more energy and move faster, resulting in an increase in pressure. Similarly, as temperature decreases, air molecules have less energy and move slower, resulting in a decrease in pressure.

## Why does air pressure decrease with altitude?

Air pressure decreases with altitude because as you go higher in the atmosphere, there is less air above you exerting pressure. This is due to the fact that gravity pulls the majority of the air molecules closer to the Earth's surface, resulting in a higher concentration of air molecules and a higher air pressure.

## How does temperature affect air pressure in different environments?

Temperature can affect air pressure differently in different environments. For example, in a closed container, an increase in temperature will lead to an increase in air pressure because the molecules have more energy and are colliding with each other more frequently. In the Earth's atmosphere, however, an increase in temperature usually leads to a decrease in air pressure due to the decrease in air density as molecules move faster and spread out.

## Can temperature changes cause extreme changes in air pressure?

Yes, temperature changes can cause extreme changes in air pressure. For example, in a thunderstorm, a rapid increase in temperature can lead to a sudden drop in air pressure which can result in strong winds and intense storm conditions. Similarly, during a cold front, a rapid decrease in temperature can cause a significant increase in air pressure resulting in strong winds and potentially severe weather.

## How does air pressure affect weather patterns?

Air pressure plays a crucial role in weather patterns. High air pressure usually indicates clear, dry weather, while low air pressure often signifies cloudy, rainy, or stormy weather. This is because air moves from high pressure areas to low pressure areas, resulting in changes in wind patterns and moisture levels, which can lead to different types of weather conditions.

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