Thermodynamics of a Box

[Rusty55125]

Does anyone have a simple equation to calculate the steady state temperature inside a box knowing the insulation qualities of the box, the initial temp, surrounding temp as well as the heating source?
I am trying to do a rough calculation on what temperature will be achieved inside this sealed box if I have a know heat source and box insulation qualities. I am not looking at accurate numbers, just a comparison of different possible heat sources and what effect they might have. I will be going some experimentation on the current heating source so I have a basic understanding on what to expect if I change the heating source.
The box materials are a simple polypropylene, the heat source is a lighting ballast 50watts and the outside temperature is 72F.
Any help would be appreciated.

 

[BigInch]

Find the heat transfer coefficient of the poly. say it = 0.2 Btu/h-ft2-Fº/in

Thickness of wall = 1 in

Take the surface area of the box = 10 ft2
heat out = 0.2 x 10 x 1 ft2-in Btu/h-ft2-Fº/in
heat out = 0.2 x 10 x 1 Btu/h-Fº
heat out = 0.2 x 10 x 1 Btu/h-dT Fº
heat out = 2 Btu/h-dT Fº
heat out/Fº = 2 Btu/h x dT Fº

heat in = 50 W x 3.412 Btu/h-W
heat in = 170.6 Btu/h

Temp stabilizes when heat in = heat out
170.6 Btu/h = 2 Btu/h x dT

170.6/2 = dT
dT = 85.3 ºF
T = 72 + 85.3
T = 157.3ºF

lesson: use a smaller box if you want to boil water with 50 W.

Going the Big Inch!

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