How the find the temp of the middle plate

[5carola5]

Homework Statement

We are having two the same metal plates. Plate one is having a temp of 127 degree celsius and plate two is 27 degrees celsius. Then a third plate, the same as the other two, is paced in the middle. What is his temperature?

Homework Equations

Don't really know. Maybe :Q=cA(T1⁴-T2⁴) or E=σT⁴ or something like those, but really I don't know

The Attempt at a Solution

first thing popping in my mind was: 127+27/2 =77 degrees celsius, which was wrong (it should be 87 degrees celsius). Then I did a lot of random stuff that doesn't really make any sens what so ever (sometimes it helps me to just write down stuff). And now I don't have any idea left anymore. I think I already spent about 1 to 1,5 hours on this one in the course of two days... ^^'


Thanks so much in advance for any help:)

 

[CWatters]

Try Kelvin in the formulae.

 

[5carola5]

I did... didn't work out for me...

 

[LawrenceC]

It's a steady state situation so the heat transfer from plate to plate must be equal. Set up the flux equation in Kelvin degrees such that the hot plate radiates to the new plate which then radiates to the low temperature plate. Solve for center plate temperature then convert back to C degrees.

 

[5carola5]

Oke this is going to sound stupid but oke: What is a flux equation? My textbook (three sheets of paper home made by the teacher) is not saying anything about them... ^^'

 

[LawrenceC]

Draw a picture and place the hot plate on the left, the plate with the unknown temperature in the middle and the low temperature plate on the right. Let the temperature of the middle plate be Tm. Hot plate is Th, and cold plate plate is Tc. You can write one equation that describes the heat transfer (flux) between middle plate and other two plates. The only unknown will be Tm. Because it's steady state, the heat transfer between plates is the same. The heat that passes from the hot plate to the middle plate equals the heat that passes from the middle plate to the cool plate.

Big hint: It will be a 4th order equation based on your equations above. Q is flux.