Heating/cooling a volume of air.

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In summary, you would need to know the temperature of both the air and the box in order to determine the amount of time it would take to heat the air to the desired temperature.
  • #1
rolinger
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I have a box that is 5'w x 5'l x 3.3'h and the air temperature within the box is 60F. If I have a device that can heat the air in the box to 80F in 7 minutes, then what formula could I use to determine how long it would take that same device to heat a box exactly 3 times the size of the first box (15'w x 15'l x 10'h) from 60F to 80F?

I know its not going to be a linear (7min x 3 = 21 min) equation because larger volumes of gas or liquid take longer to cool or heat than smaller volumes.

In addition, could this same formula be applied to determine how long it would take either boxes to heat from 60F to 90F, or possibly to cool from 90F to 50F? I am hoping to find a general formula that can be applied to a variety of heating/cooling scenarios.

Thank you.
 
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  • #2
You're going to need a little more information to apply the right heat transfer formula. What is the current dominant mechanism when heating the box? Natural convection? Forced convection? Radiation?
 
  • #3
In simple terms (assuming the air mixes and is well insulated) it is linear.
But it is not 3x, the second box is not3 times the volume it is 27 times (3x3x3) the volume so will take 27times as long to heat the air.
In the real world there are probably losses from the surfaces which are 9 times as large so it will take a bit longer than 27x.
 
  • #4
rolinger said:
I have a box that is 5'w x 5'l x 3.3'h and the air temperature within the box is 60F. If I have a device that can heat the air in the box to 80F in 7 minutes, then what formula could I use to determine how long it would take that same device to heat a box exactly 3 times the size of the first box (15'w x 15'l x 10'h) from 60F to 80F?

I know its not going to be a linear (7min x 3 = 21 min) equation because larger volumes of gas or liquid take longer to cool or heat than smaller volumes.

In addition, could this same formula be applied to determine how long it would take either boxes to heat from 60F to 90F, or possibly to cool from 90F to 50F? I am hoping to find a general formula that can be applied to a variety of heating/cooling scenarios.

Thank you.

If the heater is at a much higher temperature of the box then the power transferred per unit time should be roughly constant. In which case you can assume

[tex]\Delta T = C_p V_1 P_{heater} t_2 \Delta[/tex]

[tex]\Delta T = C_p V_2 P_{heater} t_1 \Delta[/tex]
[tex]C_p[/tex] is the specific heat
[tex]V_1[/tex] is the volume of box 1
[tex]V_1[/tex] is the volume of box 1
[tex]\Delta T[/tex] is the change in temperature.
[tex]t_1[/tex] is the time to heat box 1
[tex]t_2[/tex] is the time to heat box 2
[tex]P_{heater}[/tex] is the power of the heater.

You cannot apply the same equation to cooling because you would need more information as the above poster mentioned. See:
http://en.wikipedia.org/wiki/Heat_conduction#Newton.27s_law_of_cooling
 
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  • #5
Some more info to assist the question:

I have a fan that disperses air at 8 CFM, the air is heated to 80 F.

Assuming a fully insulated box that is 5'x5'x3 = 75 Cubic Feet. Thus 75CF / 8CFM = 9.3 minutes to heat, but this basic equation doesn't take into account the existing temperature of the air in the box.

The same equation should apply to a 15'x15'x10 box. 2250CF / 8 CFM = 4.7 hours, again, not taking into account the current temperature of the box.

If the known temperature of either box is exactly 60F...this should be enough info to compute a more accurate amount of time to heat the box, right?
 

1. How does heating/cooling a volume of air affect its pressure?

Heating a volume of air will cause its molecules to gain energy and move faster, resulting in an increase in pressure. Conversely, cooling a volume of air will cause its molecules to lose energy and move slower, resulting in a decrease in pressure.

2. Can heating/cooling a volume of air change its density?

Yes, heating a volume of air will cause its molecules to spread out and take up more space, resulting in a decrease in density. Cooling a volume of air will cause its molecules to come closer together and take up less space, resulting in an increase in density.

3. What is the effect of humidity on heating/cooling a volume of air?

Humidity is the amount of water vapor present in the air. Heating a volume of air will increase its capacity to hold water vapor, resulting in a decrease in humidity. Cooling a volume of air will decrease its capacity to hold water vapor, resulting in an increase in humidity.

4. How does the temperature of the surrounding environment affect the heating/cooling of a volume of air?

The temperature of the surrounding environment can affect the heating/cooling of a volume of air through convection. Warmer air will rise and cooler air will sink, causing a circulation of air and resulting in a more efficient transfer of heat.

5. What factors can impact the rate at which a volume of air heats/cools?

The rate at which a volume of air heats/cools can be impacted by factors such as the type of heating/cooling system used, the size and insulation of the space, the outdoor temperature, and the air flow within the space. Other factors such as humidity, altitude, and the presence of other gases can also play a role.

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