# Heat Conduction Question

## Homework Statement

A cubical box 22cm on a side is constructed from 1.3cm -thick concrete panels. A 100 W lightbulb is sealed inside the box. What is the air temperature inside the box when the light is on if the surrounding air temperature is 20 C?

## Homework Equations

rate of heat transfer : heat / delta small t = (k*A*delta big T)/ L

Where : k = characterizes the material : (in this case its concrete) : 0.8 W/m K
L = Thickness of the panels : .013m
A = cross-section area = s^2 : (.22m)^2 = .0484

## The Attempt at a Solution

100 W = ((0.8)(.22)^2(Tin - 20 C)) / .013m // the 20 C is the Tout

Tin = 53.5754 = 54 Degrees Celsius.

According to Mastering Physics this is the incorrect answer. To me it makes sense, and after reviewing my work, I cant' seem to find the error. Any help will be greatly appreciated.

-UMDstudent

A cube has 6 sides.

Right but its asking for the cross sectional area of a cube. If i use A = s^6 : (.22)^6 = .000113 = very low number. Once this is plugged into the above equation, I get a HUGE number for degrees Celsius which makes no sense.

That HUGE number = 539,019 degrees Celsius.

-UMDstudent

Why use A=s^6 ?
The total area through which the heat passes is equal to the area of one side of the cube multiplied by 6.
Total area A =6 x 0.22² [and not 1 x 0.22² as you originally calculated]
The rest of your reasoning is fine.
100 = 0.8 x A(Δθ)/0.013

Which will give you a temperature difference 6 times less than the one you originally calculated, with Tin being correspondingly much lower.

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