Slab thickness, radiation intensity

Lambert-Beer Law. The radiation intensity of a beam propagating through an absorbing slab is reduced exponentially, as a function of slab thickness y and slab absorption coefficient kx ... 

A 4.0-cm-thick slab of stainless steel (18% Cr, 8% Ni) is initially at a uniform temperature of 0°C with the left face perfectly insulated as shown in the accompanying figure. The right face is suddenly raised to a constant 1000°C by an intense radiation source. Calculate the temperature distribution after (a) 25 s, (b) 50 s, (c) 100 s, (d) an interval long enough for the slab to reach a steady state, taking into account variation in thermal conductivity. Approximate the conductivity data in Appendix A with a linear relation. Repeat the calculation for the left face maintained at 0°C. 

The absorption of x-rays is governed by the expression, I/Iq = where Iq is the intensity incident on a slab of thickness x, / is the transmitted intensity, and p is the absorption coefficient. The mass absorption coefficient is defined by p/p where p is the density. Compare the trans-mittances of 1.0 cm slabs of each of the following elements. The mass absorption coefficient is for radiation with 2 = 20 pm. 

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