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# A body coated black at 600Ksurrounded by atmosphere at 300K  has cooling rate ${r}_{0}$ the same body at 900K surrounded by the same atmosphere will have cooling rate

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a
4r0
b
16r0
c
16r03
d
81r016
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detailed solution

Correct option is C

Stefan's law is E=σT4-T4s, here E is energy radiated by a black body, σ is stefan's constant,T is temperature of the body  for given temperature T1,T2 E1E2=T14-Ts4T24-Ts4 substitute the given temperature and cooling rate E1=r0 in the above equationr0E2=6004-30049004-3004⇒r0E2=64-3494-34=1296-816561-81=12156480=316 E2=16r03

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