What is the surface area of the filament? heat expansion and transfer

[teggenspiller]

Homework Statement

the filament of a light bulb has a temperature of 2580Cel. and radiates 60W of power. The emissivity of the filament is 0.36. What is the surface area of the filament?

Homework Equations

P= $$\sigma$$*A*emissivity*T^4


A=?
$$\sigma$$=$$\sigma\ =\ 5.670400(40)\ \times\ 10^{-8}\ W\ ^{-2}\ K^{-4}$$
T=2580C and for this equation we need to use the absolute K temp, which is 2580+273, so it is 2583K
P=60, so set the equation to 60
and e= .36

The Attempt at a Solution

60W=A*$$\sigma\ =\ 5.670400(40)\ \times\ 10^{-8}\ W\ ^{-2}\ K^{-4}$$*(.36)*(2583 ^4)

and when I solve for A i get hugely long decimals (obviously), by dividing 60 by this huge number. the multiple choice answers are


a)44mm^2
b) 62
c) 74
d) 91
3) 144

all in mm^2

 

[Dick]

Well, for one thing 2580+273 is 2853, not 2583. For another your units on sigma are wrong. But most importantly, yes, you get a rather small number. What do you get? But that's the area in m^2. How many mm^2 in a m^2?

 

[teggenspiller]

wait, how are they wrong? its what physics forums gave me?

 

[Dick]

wait, how are they wrong? its what physics forums gave me?

Did they?? Then that would be wrong. If you want sigma*emissivity*A*T^4 to come out in watts then sigma should have units W/(m^2*K^4). But that's not the important part for your problem. How many m^2 do you get?? A small number in units of m^2 is a large number in mm^2.

 

[teggenspiller]

yes but i am getting 1.8*10^12 in Meters, and its not an option when converted to mm

 

[Dick]

yes but i am getting 1.8*10^12 in Meters, and its not an option when converted to mm

Now how are you getting that?? That's nowhere near 60/(0.36*sigma*(2853)^4). You really need to show more of what you are doing before anyone can figure out what you are doing wrong.

 

[teggenspiller]

hmm,..okay i love how as soon as i decide to show some work and show u what I am puttin in my calculator i get an answer that's actually a multiple choice answer. wth!? i got 44mm^2

 

[Dick]

hmm,..okay i love how as soon as i decide to show some work and show u what I am puttin in my calculator i get an answer that's actually a multiple choice answer. wth!? i got 44mm^2

So do I.

 

[teggenspiller]

your username fits
no pun intended

 

[Dick]

your username fits



no pun intended

I'm not sure what that means but I'm guessing it's not "thanks for helping".

 

[teggenspiller]

thanks a lot for you help. i suddenly understand.

 

[teggenspiller]

really though, i do appreciate it

 

[Dick]

really though, i do appreciate it

Very welcome.