Stefan–Boltzmann law
Introduction:
This is an example of the so-called “back-of-the-envelope” calculation that physics majors are trained to
perform. This one could be grasped by most 2
nd
year college physics majors. Skip it if you wish. I did it
because I teach that Mars has much less greenhouse warming than Earth, and I just wanted to see so for
myself.
Excerpts taken from Wikipedia, the free encyclopedia
The Stefan–Boltzmann law, also known as Stefan's law, states that the total energy radiated per
unit surface area of a black body in unit time (known variously as the black-body irradiance,
energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth
power of the black body's thermodynamic temperature T (also called absolute temperature):
The irradiance j* has dimensions of energy flux (energy per time per area), and the SI units of
measure are joules per second per square metre, or equivalently, watts per square metre. The SI
unit for absolute temperature T is the kelvin.
The Stefan–Boltzmann law, also known as Stefan's law, states that the total energy radiated per
unit surface area of a black body in unit time (known variously as the black-body irradiance,
energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth
power of the black body's thermodynamic temperature T (also called absolute temperature):
To find the total absolute power of energy radiated for an object we have to take into account the
surface area, A(in m2):
The constant of proportionality σ, called the Stefan–Boltzmann constant or Stefan's constant, is
non-fundamental in the sense that it derives from other known constants of nature. The value of
the constant is
where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum.
Thus at 100 K the energy flux density is 5.67 W/m2, at 1000 K 56,700 W/m2, etc. Here another
constant is included to account for imperfect or “gray” blackbodies. The constant, ε<1 for such
gray bodies, but we shall set ε = 1 and make the simplifying assumption that planets are perfect
black bodies.
