if a sphere originall radiates 100 J/s how much energy will itradiate per second

Question

if a sphere originall radiates 100 J/s how much energy will itradiate per second if its absolute temperature is doubled and itsdiameter is halved? (neglect any heat transfer into thesphere) the answer is is 400J/s. but do not know how to get that ??help please if a sphere originall radiates 100 J/s how much energy will itradiate per second if its absolute temperature is doubled and itsdiameter is halved? (neglect any heat transfer into thesphere) the answer is is 400J/s. but do not know how to get that ??help please

Explanation / Answer

The energy radiated per second is given as    P = e A T4 Area A = d2 / 4 So the above formula    P = e (d2 / 4)T4 energy / sec is proprotional to square of the diameterand fourth power of absolute temperature For two different cases    P1 = d12T14 P2 = d22T24 The ratio is P2 / P1 = d22 T24 /d12T14    Given that P1 = 100J , d2 =d1 /2 and T2 = 2T1     P2 / 100 J = ( d12 /4) (16 T14 ) / d12T14    P2 /100 = 4     P2 = 4x 100J          = 400J P2 / P1 = d22 T24 /d12T14    Given that P1 = 100J , d2 =d1 /2 and T2 = 2T1     P2 / 100 J = ( d12 /4) (16 T14 ) / d12T14    P2 /100 = 4     P2 = 4x 100J          = 400J

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