Heat-Transfer Mechanisms (HARD)

[spaghed87]

Homework Statement

What maximum power can be radiated by a 14cm -diameter solid lead sphere? Assume an emissivity of 1

Answer in two sig fig.

Homework Equations

( Q / delta t) = e*σ*A*T^4

e=1
σ=5.67*10^-8 W/m^2*K^4 Stefan-Boltzmann constant (<--- who happens to be my great grandpa ;) )

A= (4*pi*r^2) = (4*pi*0.07m^2)
T= 273K (I think)

The Attempt at a Solution

( Q / delta t) = e*σ*A*T^4 = (1)*(5.67*10^-8w/m^2*k^4)*(4*pi*0.07m^2)*(273k^4) = 19 Watts

They never gave the temperature so I was assuming it would be 273. They do mention that it is a lead sphere and I have not used any values for the physical properties of lead in my equation. I think I am probably off on the temperature. Does anyone have some input? This is masteringphysics homework so I need use their values or I could get my answers wrong due to different values for the constant. I am not asking for answer... just guidance... I think I am very close. I have 48 hours left so any input asap would be appreciated.

-Eddie

 

[mal4mac]

Boltzmann is your great grandpa! Wow. I recently read "Boltzmann's atom" by David Lindley, I recommend it for light reading. It won't help with solving this though...

Do you not need Wien's law as well? To find the temperature that gives maximum power? You might need to look up peak wavelength for lead...

 

[spaghed87]

Nope, I just was assuming it would max out at power at room temperature because I was confused and like a drone just was plugging in 273K. Bad idea... Actually, lead melts at 601 kelvin and that means that the sphere will no longer be solid at that temp. Thus, the max power that can be radiated for a solid will be the change in t from 0K to 601K. I just solved the problem on my own. I just had to sleep on it. ;)