Iron Bar Thermal Radiation Calculation

[Gaith]

Homework Statement

Energy can be transmitted via radiation, the rate at which this happens is H=σAT⁴. A bar of iron is 0.5m long, 0.2m wide and 0.2m high. Iron has a density of 7900 kg/m³, a heat capacity of 400J/kgC, and a coefficent of linear expansion of 1.2x10^-5

What is the rate at which iron radiates energy assuming it is initially at 500K and that the emissivity is 0.8?

Homework Equations

H=σAT⁴

The Attempt at a Solution

I started by trying to figure out the final Temperature so I could plug it into the formula above and get the H. However I am stuck at which equation to use in order to find the final temperature.

Im not sure if I'm going about it the right way either. Help would be greatly appreciated. Thank you

 

[Simon Bridge]

You don't need the final temperature, the formula does not call for it.

 

[Gaith]

You don't need the final temperature, the formula does not call for it.

Ok so you're telling me I can just plug in the numbers and get the answer like this

H=(5.67x10^-8)(0.8)(0.2x0.5)(500)^4

The answer is still incorrect...

 

[SteamKing]

Ok so you're telling me I can just plug in the numbers and get the answer like this

H=(5.67x10^-8)(0.8)(0.2x0.5)(500)^4

The answer is still incorrect...

Think carefully about what area A represents in the formula for the thermal radiation. Does heat only radiate from one side of the iron bar?

 

[Simon Bridge]

How did you work out the total surface area of the block of iron?
Ah, HM beat me to it.

 

[Gaith]

Think carefully about what area A represents in the formula for the thermal radiation. Does heat only radiate from one side of the iron bar?

Wow I can't believe how I didnt see that. Thank you for pointing out my stupid mistake!