Hi having problems with this question, any guidance on how i can solve would be very much appreciated

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.

let try...

use kirchhoff's law to determine the emitting radiance.

the kirchoff's law is basically at any non-zero temperature, an object body would emitted electromagnetic radiation. so when an object emitted at thermodynamic equilibrium, the total emission should be the same as total absorption. that's kirchoff's law.

in simplify.

emission = absorption.

the emissivity at a particular wavelength is given by

E = emitted radiation / black body temperature.

and the emitted radiation is given by
ER = energy density * speed of light / 4

back to kirchoff's law.

since object emitted energy should also be absorbed with the same amount back (ie, conservative of energy).

so,

emitted radiation = emissivity * black body temperature = absorption wavelength * incidental radiance.

simply in all. ER = E * B = A * I

1) incidental radiance = E*B / A

E = emissivity
B = black body tempt
A = absorption

2) emitted radiation (same as irradiance) by the slab...

ER = energy density * speed of light / 4

3) using wien displacement law.. to solve

wavelength = b/T
b = wien constant, which is something 2.9 x 10^6 Knm