Blackbody Radiance: Calculate Absorption & Emission Rates & Equilibrium Temp

[beasht]

Homework Statement

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.


justing looking for some pointers to get started such as formulas, etc that are best suited for this problem, and guidance on the steps i need to take,
any info much appreciated,
thanks

 

[NateD]

Homework Equations Stefan-Boltzmann Law: I=σT^4 The Attempt at a Solution1. To find the rate at which the slab will warm up, you will need to use the Stefan-Boltzmann law to calculate the irradiance of the incident radiation. Then, you can use the absorption coefficient, density and heat capacity of the slab to compute the rate of energy absorbed by the slab. 2. To calculate the rate at which the slab cools by emission, you will again need to use the Stefan-Boltzmann law to calculate the irradiance emitted from the slab. Then, you can use the absorption coefficient, density and heat capacity of the slab to compute the rate of energy emitted. 3. To calculate the equilibrium temperature, you will need to set the rate of energy absorbed by the slab equal to the rate of energy emitted by the slab. Then, you can solve for the equilibrium temperature.