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Two spherical black bodies of radii R(1)...

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. `R_(1)//R_(2)` must be equal to

A

`(T_(1))/(T_(2))`

B

`(T_(2))/(T_(1))`

C

`(T_(1)/T_(2))^(2)`

D

`((T_(2))/(T_(1)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`(Q)/(t)=sigma A T^(4)`
i.e, power `=sigmaAT^(4)`
`therefore` for same power
`therefore A alpha (1)/(T^(4))`
`therefore (A_(2))/(A_(1))=(T_(1)^(4))/(T_(2)^(4))`
`therefore (4pi r_(2)^(2))/(4pir_(1)^(2))=(T_(1)^(4))/(T_(2)^(4))`
`therefore (r_(2))/(r_(1))=((T_(1))/(T_(2)^(2))`
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