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The radiant emittance of a black bodyt i...

The radiant emittance of a black bodyt is `R=250kW//m^(2)`. At what wavelength will the emmisivity of this black body be maximum? `(b=2.9xx10^(-3)m.K` and `sigma=5.67xx10^(-8)Wm^(-2)K^(-4)`)

Text Solution

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Using Stepan's law we have
`R= sigmaT^(4)`
`rArr T =((R )/(sigma))^(1//4)`
`=((250 xx 10^(3))/(5.67 xx 10^(-8)))^(1//4)`
`= 1.449 xx 10^(3)`
= 1449 K
Now using Wein's displacement law, the maximum spectral radiance will be at wavelength `lambda_(m)` given as
`lambda_(m) =(b)/(T) =(2.89 xx 10^(-3))/(1449) = 19.9447 xx 10^(-7) m`
= 19944.7 A
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