hi guys

 

Does anybody know what formula one would use to calculate how long it would take to raise the temperature of an area of x litres of air by blowing in y litres of warmer air . ie if I blow in air at 25 degrees C into an area which is at 20 degrees C , how long would it take to raise the temperature by one , two or three degrees?

 

What I know is the volume of air (in litres) blowing in as well as the volume of air in the area (in litres) as well as the two different temperatures of both of these areas.

 

Thanks guys:-)

is the air being displaced or pressurised?

You would also need to know the heat capacity of the other objects in contact with the air.

Displaced, im just blowing air from one room to another room through a small fan...

Well if the pressure is staying the same then there is no heating due to pressurisation.

 

As it's just air and air you don't need to worry about the specific heat capacities, unless you're taking in to account heat loss through the walls and to objects in the room etc.

 

But in it's simplest case: if you have 1litre of air at 20C, and add another litre of air at 25C, then overall you get two litres of air at 22.5C.

 

But if you're keeping the volume constant, then if you filled half your room with the warmer air, then let the two parts (hotter and colder) mix, then overall the temperature would again average at 22.5C.

 

If you're dealing with just air (not different materials, not worrying about heat loss etc.) then it's just like doing a weighted average. So if have 1L of air at 20C, and displace 1/5 of that out and replace it with 1/5L of 25C air, then let it all mix and come to an equilibrium, then the temperature will be 21C.

5614 has given the answer I was going to if you said displaced... Ignoring loses to objects in the room... The biggest apparent difference (to humans) will be due to the wall temps...

If no pressure exists, NO MOVEMENT of air can take place, eh?

 

Pressure makes fluids move. If they are constrained, that is, cannot move, then they are compressed by the pressure.

 

Hence, a "monkey-wrench" has been thrown into the mix. imp

If no pressure exists, NO MOVEMENT of air can take place, eh?

 

Pressure makes fluids move. If they are constrained, that is, cannot move, then they are compressed by the pressure.

 

Hence, a "monkey-wrench" has been thrown into the mix. imp

 

Pressure gradients = flow...

 

So you will get an average pressure increase in the room, turning the fan off it will return to what it was, and the pressure increase wont be enough to raise the temperature compared to the warm air...

It'll be different if you are continually introducing that warm air at some rate, since that involves solving a differential equation.