A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. What would be the power of radiation if radius were to be halved and the temperature is doubled ?

Options

A. 1800 W
B. 2000 W
C. 1500 W
D. 1200 W

Answer

A

Explanation

Energy radiated/sec = Radiated Power
`E=AsigmaT^(4)=(4piR^(2))sigmaT^(4)" "`(Stefan's law)
In the second case, `R'=R/2andT'=2T`
`thereforeE'=4pi(R/2)^(2)xxsigmaxx(2T)^(4)`
`=4piR^(2)xxsigmaT^(4)(1/4xx16)=4E`
`thereforeE'=4xx450=1800W`