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A body at 300 degree celcius radiates 10 joules/sq.cm -sec.If sun radiates 100000joules/sq.cm-sec,then its temp is

A body at 300 degree celcius radiates 10 joules/sq.cm -sec.If sun radiates 100000joules/sq.cm-sec,then its temp is

Grade:12

2 Answers

AskIITians Expert Hari Shankar IITD
17 Points
11 years ago

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

 

Ramesh V
70 Points
11 years ago

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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IIT Kgp - 2005 batch

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