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Energy radiated is proportional to T4 (Stefan-Boltzmann law)
Let E = kT4
Then, For the first body, 10 = k(573)4
(Because we 300 C = 300+273 = 573 K)
Therefore,
k = 10/(573)4 = 9.27 x 10-11
For the case of the sun,
E = 100000.
So,
100000 = (9.27 x 10-11)T4
or, T4 = 100000/(9.27 x 10-11) = 1.08 x 1015
So T = (1.08 x 1015 )1/4 = 5732.65 K
By Stefan-Boltzmann law,
energy of thermal radiation emitted per unit time by a black body of surface area A is given by:
U= kAT4
T2 = 573K and U1=105 , U2=10
so for given conditions, U1/U2 = (T1/T2)4
T1 = 5730 K
Temp. of sun = 5457 C
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