(7) (i) Normal human body temperature is 98.6◦ F = 37.0◦ C = 310 K. Assuming that human skin is a perfect thermal radiator (with efficiency ε = 1), determine the wavelength of the maximum intensity of electromagnetic radiation that a human being radiates, in microns.
(ii) Suppose someone is running a fever of 102.0◦ F. How much more power (in Watts) does this person radiate than when this person is at normal human body temperature, assuming the fever causes no swelling or edema, or emaciation? Remember that for thermal radiators, intensity
I = σT4, where σ is the Stefan-Boltzmann constant and T is temperature in Kelvins.
(iii) In 1900, by assuming that E = nhf where n = 1, 2, 3 . . . , Max Planck derived the correct formula for the spectrum thermal radiation, also called Planck radiation or blackbody radiation. Planck’s formula is:
I(λ,T) = 2πhc2 λ5[exp( hc ) − 1]
λkB T
Derive Wien’s law, also called Wien’s displacement law, from this formula.
- 7 I Normal Human Body Temperature Is 98 6 F 37 0 C 310 K Assuming That Human Skin Is A Perfect Thermal Radiat 1 (32.75 KiB) Viewed 41 times
(7) (i) Normal human body temperature is 98.6° F = 37.0° C = 310 K. Assuming that human skin is a perfect thermal radiator (with efficiency = 1), determine the wavelength of the maximum intensity of electromagnetic radiation that a human being radiates, in microns. (ii) Suppose someone is running a fever of 102.0° F. How much more power (in Watts) does this person radiate than when this person is at normal human body temperature, assuming the fever causes no swelling or edema, or emaciation? Remember that for thermal radiators, intensity I=oT¹, where o is the Stefan-Boltzmann constant and T is temperature in Kelvins. (iii) In 1900, by assuming that E = nhf where n= 1,2,3..., Max Planck derived the correct formula for the spectrum thermal radiation, also called Planck radiation or blackbody radiation. Planck's formula is: 2 hc² I(A, T) = A5[exp()-1] Derive Wien's law, also called Wien's displacement law, from this formula.