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If the temperature of the sun were to in...

If the temperature of the sun were to increase form T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be

A

4

B

16

C

32

D

64

Text Solution

Verified by Experts

The correct Answer is:
D
By Stefan.s law, Radiant energy ` prop AT^4`
since ` A prop R^2 therefore ` Energy ` prop R^2 T^4`
`(" finally radiated energy ")/( "Initially radiated energy ") =(R_(2)^(2) . T_(2)^(4))/( R_(1)^(2) .T_(1)^(4))`
` therefore ` RAtio `= ((R_2)/(R_1)) ^2 ((T_2)/(T_1))^4 = ((2R)/( R))^2 . ((2T)/(T))^4`
` therefore ` Ratio `= 4 xx 16 = 64`
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