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test2k8
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Consider a slab of matter contained within two infinite planes a distance of s = 1m apart.
absorption coefficent =1m2kg-1
density of slab 1kgm-3
heat capacity 103^3jk-1kg-1
assume the absorption coefficient to be independent of wave length
1.Suppose one face of a slab is illuminated by a source emitting blackbody radiation at temp 300k, compute the rate at which the slab would tend to warm up by absorption of incident radiance.
2. assuming the slab is also at temp of 300k compute the irradiance emitted by the slab. Compute the rate at which the slab would tend to cool by emission.
3. assuming that the incident black body radiation remains unchanged in time, compute the temp at which the slab will come into equilibrium.
given equation:
emissivity at given wavelength = Rλ / Bλ
My attempt to show with a little confusing. I believe we have to use the Kirchhoff's Law to solve this problem. From my understand..
Rλ = Emissivity*Bλ = aλ*Iλ
Rλ = emitted spectral radiance
Bλ = black body
aλ = absorptance
Iλ = incident radiance..
therefore, to find 1)
Iλ = Emissivity*Bλ / aλ??
for 2)...
Since emissivity is given by Rλ / Bλ. Therefore the actual radiance emmitted by the slab is just ..
Rλ = Bλ * Emissivity.
3) Question 3 I'm not sure how to do it..
Can you help?
absorption coefficent =1m2kg-1
density of slab 1kgm-3
heat capacity 103^3jk-1kg-1
assume the absorption coefficient to be independent of wave length
1.Suppose one face of a slab is illuminated by a source emitting blackbody radiation at temp 300k, compute the rate at which the slab would tend to warm up by absorption of incident radiance.
2. assuming the slab is also at temp of 300k compute the irradiance emitted by the slab. Compute the rate at which the slab would tend to cool by emission.
3. assuming that the incident black body radiation remains unchanged in time, compute the temp at which the slab will come into equilibrium.
given equation:
emissivity at given wavelength = Rλ / Bλ
My attempt to show with a little confusing. I believe we have to use the Kirchhoff's Law to solve this problem. From my understand..
Rλ = Emissivity*Bλ = aλ*Iλ
Rλ = emitted spectral radiance
Bλ = black body
aλ = absorptance
Iλ = incident radiance..
therefore, to find 1)
Iλ = Emissivity*Bλ / aλ??
for 2)...
Since emissivity is given by Rλ / Bλ. Therefore the actual radiance emmitted by the slab is just ..
Rλ = Bλ * Emissivity.
3) Question 3 I'm not sure how to do it..
Can you help?