Effect of air pressure on temperature

[chas209365]

Hello,
I'm posting here in an attempt to solve a practical problem involving air temperature and pressure in a home, but I'll pose the problem in a simple, hypothetical model.
Take a large, closed box with a certain quantity of air contained within. A source of heat is placed on the bottom half of the box. It heats up the air temperature, the air pressure increases, and warm air rises towards the top of the box.
My question is this: If you placed a second heat source in the upper half of the box, and made that heat source equal to or warmer than the heat source at the bottom of the box, would the increased pressure of the air in the upper half of the box prevent the warm air at the bottom of the box from rising, thereby increasing air temperature and pressure in the bottom of the box?
Thanks for any help on this basic question.
Regards,
Charlie Cavanaugh

 

[russ_watters]

Welcome to PF.

No, nothing constrains the pressure from equalizing throughout the box, so it equalizes throughout the box.

The warm air rises not because of the pressure difference (which is negligible) but because of the density difference.

 

[Calrik]

Welcome to PF.

No, nothing constrains the pressure from equalizing throughout the box, so it equalizes throughout the box.

The warm air rises not because of the pressure difference (which is negligible) but because of the density difference.

True this is more of a chemical thing than a physics thing the law that describes this do you know it OP?

Clue: air pressure/temperature and temperature and its relation to pressure.

 

[chas209365]

Thanks for your quick replies.

russ: If the pressure equalizes throughout the box, would that mean that the temperature would equalize also? I'm a little puzzled by your comment about density difference being the key factor in making warm air rise. From my understanding, cold air is denser than warm air because of decreased molecular motion. Wouldn't a substance of greater density actually prevent a substance of lesser density from moving into the space it occupies? So if density was the key factor, wouldn't cold air in the upper layers of the box actually prevent warm air from rising into its space?

Charlie

 

[Calrik]

Thanks for your quick replies.

russ: If the pressure equalizes throughout the box, would that mean that the temperature would equalize also? I'm a little puzzled by your comment about density difference being the key factor in making warm air rise. From my understanding, cold air is denser than warm air because of decreased molecular motion. Wouldn't a substance of greater density actually prevent a substance of lesser density from moving into the space it occupies? So if density was the key factor, wouldn't cold air in the upper layers of the box actually prevent warm air from rising into its space?

Charlie

Cold air doesn't rise or fall any more than warm air does. It just moves between a gradient of pressure related to temperature.

I Think you are thinking in terms of absolutes, or that air is a homogeneous entity.

 

[Nano-Passion]

The pressure would go up due to the increased temperature. The higher temperature the higher the pressure, it is a direct correlation (correct me if I'm inaccurate).

The increased temperature would be because of you putting another heat source on the limited volume of the box. Thus an increased pressure in the box.

What is not going to happen is an increased pressure on a certain area of the box; but an increased AVERAGE pressure in the whole box.

 

[russ_watters]

russ: If the pressure equalizes throughout the box, would that mean that the temperature would equalize also?

No, cold and warm air can stay somewhat separated, mixing much slower, through natural convection. If the warm air starts on top, though, convection doesn't work and the air parcels can stay pretty well separated for a long time.

I'm a little puzzled by your comment about density difference being the key factor in making warm air rise. From my understanding, cold air is denser than warm air because of decreased molecular motion.

Cold air is denser because molecular motion keeps the molecules further apart.

Wouldn't a substance of greater density actually prevent a substance of lesser density from moving into the space it occupies?

No - air is a fluid, not a solid. One parcel of air cannot prevent another parcel of air from pushing it around.

So if density was the key factor, wouldn't cold air in the upper layers of the box actually prevent warm air from rising into its space?

No - what actually happens is the more dense air doesn't have the buoyancy required to stay aloft and so it falls. That's convection.

 

[russ_watters]

Cold air doesn't rise or fall any more than warm air does. It just moves between a gradient of pressure related to temperature.

That is not correct. The pressure gradients in a room of 4m cubed will measurable only with an accurate barometer (and still inseparable from the atmospheric pressure gradient), but the temperature gradient could be pretty large - 10C or more between the floor and ceiling. No, it is temperature, not pressure, that causes stratification.

 

[russ_watters]

The pressure would go up due to the increased temperature. The higher temperature the higher the pressure, it is a direct correlation (correct me if I'm inaccurate).

The increased temperature would be because of you putting another heat source on the limited volume of the box. Thus an increased pressure in the box.

What is not going to happen is an increased pressure on a certain area of the box; but an increased AVERAGE pressure in the whole box.

Correct.