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Two spherical black bodies of radii r1 a...

Two spherical black bodies of radii `r_1` and `r_2` and with surface temperature `T_1` and `T_2` respectively radiate the same power. Then the ratio of `r_1` and `r_2` will be

A

`((T_2)/(T_1))^2`

B

`((T_2)/(T_1))^4`

C

`((T_1)/(T_2))^2`

D

`((T_1)/(T_2))^4`

Text Solution

Verified by Experts

The correct Answer is:
A
Power (P) `=A epsilon sigma T^4`
For same power
`A prop (1)/(T^4) implies ((r_1)/(r_2))^2= ((T_2)/(T_1))^4 implies (r_1)/(r_2) = ((T_2)/(T_1))^2`
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