Consider a spherical blackbody of temperature T=240 o C and radius R=0.20m that
ID: 1533652 • Letter: C
Question
Consider a spherical blackbody of temperature T=240 oC and radius R=0.20m that radiates energy to an environment of very low temperature. Suppose you surround the sphere with a black, thin, spherical shell of radius 6R. What is the temperature of the shell in Celsius when it reaches a steady state? Remember the inner surface of the large sphere is always absorbing energy from the black body and the outer surface is losing energy to the very low-temperature surroundings.
Answer is in Degrees Celsius.
Explanation / Answer
from stefan's law of radiation
rate of heat transfer = A*e*sigma T^4
here both are of emmisivity e=1
area is spheres surface area A1 = 4piR^2; A2 = 4piR2^2
sigma is Boltzman constant
T is temperature
A1*e*sigmaT1^4= A2*e *sigma T2^4
(A1/A2)T1^4 = T2^4
T2 = (A1/A2)^1/4*T1
= (R^2/6R^2)^1/4*T1
= ((0.2^2)/(6*0.2)^2)^0.25*(240+273.15)
= 209.5 k
T2 = -63.65 0C