Two bodies A and B have emissivities 0.5 and 0.8 respectively. At some temperature the two bodies have maximum spectral emissive powers at wavelength `8000 Å` and `4000 Å` respectively. The ratio of their emissive powers at these temperatures is :

Options

A. `(5)/(128)`
B. `10`
C. `(5)/(16)`
D. None of these

Answer

A

Explanation

Let the body have temperatures `T_(1)` and `T_(2)` respectively at wavelength `lamda = 8000 Å` and `lamda_(2) = 4000 Å`
`:.` From Wien's displacement law
`lamda T` = constant
`rArr lamda_(1) T_(1) = lamda_(2)T_(2)`
`8000 xx T_(1) = 4000 T_(2)`
`(T_(1))/(T_(2)) = (1)/(2)`
Emissive power `= e sigma A T^(4)`
`:.` Ratio of emissive powers at these temperature is
`=(e_(1)T_(1)^(4))/(e_(2)T_(2)^(4))=(0.5)/(0.8)xx((1)/(2))^(4)=(5)/(128)`