Pls help out as soon as possible......!!! Thanks The total (integrated) power ra

Question

Pls help out as soon as possible......!!! Thanks The total (integrated) power radiated by a blackbody at a temperature T is given by the Stefan-Boltzmann law: E = sigma T^4. This is obtained by integrating over all wavelengths(from lambda = 0 to lambda = infinity) the expression for the power radiated per unit area per unit wavelength J(lambda, T) = c/u(lambda,T), where the energy per unit volume per unit wavelength in a small wavelength range from lambda to lambda + d lambda is: Changes the variables in the above using the variable x = hc/lambda kT and using the fact that evaluate the expression for E(T) = - Show that the Stefan-Boltzmann constant sigma has the value:

Explanation / Answer

pi = 3.14

k = 1.38 e -23

c = 3e 8

h = 6.624 e -34

so

sigma = 2* 3.14^5 * (1.38*10^-23)^4/15*(6.626*10^-34)^3 *3 e8 * 3e8

sigm = 1.476 e -90/(6.626 e-34* 6.626 e-34 * 6.626e-34* 3e8 * 3e8)

sigma = 5.637 *10^-8 W/(m^2 K^4)

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