A black body is heated from 270C to 1270C. The ratio of their energies of radiation emitted will be
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a
81 : 256
b
27 : 64
c
9 : 16
d
3 : 4
answer is A.
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Detailed Solution
From Stefan's law, the total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature of the body.That is E = σT4where σ is Stefan's constantGiven,initial temperature T1 = 273 + 27 = 300 Kfinal temperature T2 = 127 + 273 = 400 KHence, we have E1E2= T14T24 = (300)4(400)4 = 81256Therefore, E1 : E2 = 81 : 256