Suppose the Sun expands so that its radius becomes 100 times its presents radius and its surface temperature becomes half to its present value. The total energy emitted by it then will increase by a factor of . . . . .. .

Options

A. 104
B. 625
C. 256
D. 16

Answer

B

Explanation

From Stefan-Boltzmanns law, we have
`E=esigmaAT^(4)`
`:.EpropAT^(4)" "(e sigma" = constant")`
`:.E prop(4piR^(2))T^(4)" "(becauseA=4piR^(2))`
`:.E propR^(2)T^(4)" "(4pi" is constant")`
`(E_(2))/(E_(1))=((R_(2))/(R_(1)))^(2)((T_(2))/(T_(1)))^(4)`
`=((1000R_(1))/(R_(1)))^(2)((T_(1))/(2T_(1)))^(4)`
`=(100xx100)/(16)=625`
`:.E_(2)=625E_(1)`