I mentioned this one briefly, but I feel I should include it here. This is the formula Max Planck used to describe the blackbody radiation curve.
The symbols in the equation are as follows:
2π = appox. 6.2832
Pλ = Power per m2 area per m wavelength
e = the base of natural logarithms: approximately 2.718281828459 (see: http://mathforum.org/dr.math/faq/faq.e.html)
h = Planck's constant (6.626 x 10-34 J/sec)
c = Speed of Light (about 3 x 108 m/sec)
λ = Wavelength (m)
k = Boltzmann's Constant (1.38 x 10-23 J/K)
T = Temperature (in °K)
All you need to know is any particular wavelength of a blackbody radiation field and its temperature--let's use 10-5 m wavelength radiation from a 1000 °K field as an example. Just plug those two things in the λ and T values and the already given values in their respective slots and you get your power per square meter per meter of wavelength. The equation is somewhat complicated, but not too difficult. The value of the equation representing our numerator, 2πhc2, equals 3.7450152 × 10-13. This value will remain the same whenever you use this equation. The value of the equation representing our denominator, λ5(exp(hc/λkT)-1), using our above example values for λ and T, will be approximately 3.2225313. Now for the simple finish. 3.7450152 divided by 3.2225313 equals about 1.1621346238, and that is our value for Pλ in this sample equation.
