In a government program designed to help Pakistan\'s insurgents, a strange test

Question

In a government program designed to help Pakistan's insurgents, a strange test is being carried out at the Johnson Metal Foundry in Bethesda, MD. Here, CIA scientists subjected a long metal plate measuring 1 meter by 100 meters is to a temperature profile in such a way that the temperature linearly increases from 0 degrees Kelvin at the left end to 1000 degrees Kelvin at the right end. If we assume the emissivity is 1, determine the total thermal energy in Watts being emitted by this piece of metal. Use your EXCEL skills in this one.

Explanation / Answer

T = alpha t

E = int(P dt)

E = int((A) sigma T^4 dt)

E = int((A) sigma T^4 (1/alpha) dT)

E = (A) sigma (T^5/5) (1/alpha)

-----------------

P_tot = E/t'

= E/(T/alpha)

= alpha E/T

= (alpha/T) * (A) sigma (T^5/5) (1/alpha)

= (1/T) * (A) sigma (T^5/5)

= (A) sigma (T^4/5)

= (1*100) * (5.67e-8) * ((1000y4)/5)

= 1.1 MWatts

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