Thermodynamics radiation problem

[composyte]

Homework Statement

A cubical box 19cm on a side is constructed from 1.4cm -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

E_th=W+Q
Q_net=Q_1+Q_2+...
E_th=N*C_v (deltaT)
(Q/delta(t))=e*(sigma)*A*T^4

The Attempt at a Solution

okay so I am thinking that I should find Q_net which will be equal to E_th to find the final temperature of the air.. And so I would use the (Q/delta(t)) equation to find the radiation emitted from the lightbulb and the radiation emitted from the concrete panels...My problem is the question doesn't give the emissivity of the concrete and nor does it say what the initial temperature for the air should be. Because of this I feel like my answer is entirely on the wrong path..Either that or the question is just expecting you to make a lot of assumptions..any help??

 

[voko]

The problem is about a steady state, when the temperature inside and outside are constant.

 

[SteamKing]

My problem is the question doesn't give the emissivity of the concrete and nor does it say what the initial temperature for the air should be.

If the surrounding air temp is 20 C, what would be a reasonable initial temp. for the air inside the box, before the light bulb is switched on? The box is not inside a refrigerator, nor has it been baked in an oven beforehand.

If your textbook doesn't have a table of emissivity values for various materials, like concrete, you should be able to find them in a handbook or online.

 

[composyte]

okay so I get N*C_v*(deltaT)=Q_1+Q_2=P*(delta t)+[e*(sigma)*A*T^4](delta t)

and I can find all of the variables, however how do I get rid of delta t? (the change in time, which is different from deltaT, the change in temperature). and I am not sure how to get the value of N (the number of mols of the air) I have the volume but not the pressure, would the pressure just be the force from the top slab multiplied by the area??

 

[SteamKing]

okay so I get N*C_v*(deltaT)=Q_1+Q_2=P*(delta t)+[e*(sigma)*A*T^4](delta t)

and I can find all of the variables, however how do I get rid of delta t? (the change in time, which is different from deltaT, the change in temperature).

You are supposed to calculate the steady-state temperature inside the box after the light has been switched on. Presumably, this is a calculation which must be done in a step-wise manner, using time as the independent variable. This is not the simple plug-and-chug type of problem which you apparently were expecting.

and I am not sure how to get the value of N (the number of mols of the air)

You know everything that is required to calculate the number of moles of air inside the box. (See comment below)

I have the volume but not the pressure, would the pressure just be the force from the top slab multiplied by the area??

What force?

The box presumably is surrounded by the Earth's atmosphere... what is the pressure there? AFAIK, it's not an air-tight box.

 

[voko]

As has already been indicated, this is a steady-state problem. Now think about this: there is a source of energy that is constantly ON inside the box, yet the temperature inside is not rising. How can this be possible?