Integrating the blackbody equation over wavelength gives the Stefan-Boltzmann La

Question

Integrating the blackbody equation over wavelength gives the Stefan-Boltzmann Law for the total power emitted by a blackbody of surface area A and temperature T: R(T) = epsilon sigma T^4 (where the emissivity epsilon is taken to be 1 as appropriate for a blackbody). Planck calculated R(T) in terms of h, k_B, and c R(T) = integral (lambda, T) d lambda = 2 pi^5k^4_B/15h^3c^2 T^4 and found the experimentally known value of sigma = 5.7 Times 10^-8 W/m^2/K^4. The human body has an area of ~ 2 m^2 and a skin temperature of ~ 33 degree C. Calculate the power radiated by such a body. Does this seem reasonable

Explanation / Answer

The power radiated by the body is

P=(sigma) ×(e)×T4

= 5.7×10-8×1×(33+273)

= 4.62×10-6 W/m^2

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