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An object is at temp of 400 degree celcius.At what temp would it radiate energy twice as fast?The temp of the surroundings may be as sumed to be negligible

An object is at temp of 400 degree celcius.At what temp would it radiate energy twice as fast?The temp of the surroundings may be as sumed to be negligible

Grade:12

1 Answers

AskIITians Expert Hari Shankar IITD
17 Points
12 years ago

By STefan-Boltzmann law, Rate of heat radiation E is proportional to T4 .

Let E = kT4.

Also, let the iniotial energy radiated be E1.

Temperature T = 400 C = 400+273 K = 673 K

So, E1 = k (673)4 .................(1)

Let rate of heat radiation be 2E1 at temperature T2.

Then, 2E1 = k(T2)4

2E1 = [E1/(673)4] (T2)4 using (1)

(T2)4 = 2 (673)4

T2 = (2)1/4 * 673 = 1.19 * 673 = 800.33 K

 

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