Question

A room gives out 87 MJ heat every day. A company wants to make an electrical heater to maintain a constant temperature in the room. How long of a nichrome 1mm diameter wire would heating element need?

Answer 1

I am completely at loss here. I think that at some point the formula \[R = \frac{length * ro}{diameter}\] (ro as in a greek letter) would be useful, but I have no idea how to convert heat into anything useful...
@ganeshie8

Answer 2

that'll give you the resistance for a certain length and x-sect area

you need more info - eg voltage

Answer 3

link the actual question if you can. it's based on the same idea as the others you posted earlier but info is missing :-(

Answer 4

Well, info isn't missing. That's why I posted this here.

Answer 5

I think that, perhaps, we could figure something out of a word "constant temperature", but I am not sure.
Also, it is possible that the answer should be expressed in letters (although I doubt that).

Answer 6

Just googled, seems that ro is between 1 and 1.5 * 10^-6. We can use constants.

Answer 7

So, the only thing that is missing - how to take out resistance out of heat?

Answer 8

in letters

if you are using a fixed voltage \(V\), the power is \(P = \dfrac{V^2}{R}\) -- that's what they mean, the power loss is heat. or \(P = IV = I^2 R\)

So with \(R = \dfrac{\rho L }{A}\)

so

\(\Large P = \dfrac{V^2}{\dfrac{\rho L }{A}} = 87*10^6\)

with \(\Large A = \dfrac{\pi (0.001)^2}{4}\)

you an find the resistivity online somewhere so....play with that and L is the only unknown provided you have a V

Answer 9

Oh crap. Howler alert!!

"A room gives out 87 MJ heat **every day**."

So power P is actually \(P = \dfrac{87.10^6}{24*60*60} ~ J/s\)

So the power the heater must supply to compensate is

\(\large P = \dfrac{V^2}{\dfrac{\rho L }{A}} \approx 1007\) and solve for L

but you still have an unknown in there. you need to know the voltage or current