Heat Conduction Question

[UMDstudent]

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

 

[Stonebridge]

A cube has 6 sides.

 

[UMDstudent]

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

 

[Stonebridge]

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.