• A solid object emits light if it is warmer than ``absolute zero'' temperature. The emitted spectrum is characteristic of the object's temperature.

• Special case: A Blackbody - an object that is perfectly black (i.e. that it absorbs all light incident upon it) when it is cold.

• Most solid objects are good approximations to blackbodies.

• Stars (which are dense balls of hot gas) also behave like blackbodies.

• The peak of a blackbody's spectrum is determined by its temperature

So, don't get confused about the term "blackbody". It is an unnecessary idealization from the perspective of this course. Here is a clarification I sent recently.

• ...It means you shouldn't even think about the term "blackbody" and just focus on the idea that hot solid objects glow and that the hotter they are the bluer the radiation (the equation with T in the denominator) and the hotter they are the brighter they get (the equation with T to the 4th power). The point is that nothing is a true blackbody, but they are all close enough (including stars) that these equations apply.

• The hotter the object the ``bluer" the light.
• The Sun (6000oK) emits most of its radiation at visible wavelengths (0.5 m).
• Room temperature objects (300oK) emit most of their radiation at infrared wavelengths (10 m).

### The Stefan-Boltzmann Law

• The total energy emitted by each of the surface of a blackbody depends only on the temperature.

i.e. If you double the temperature of a blackbody the amount of energy radiated goes up 16 times!

• Sunspots provide a vivid example of the Stefan-Boltzman law in action.

• Sunspots are only about 1000 degrees cooler than the surrounding 5800K solar surface. Even though the difference in temperature is 4800K vs. 5800K, raising this number to the fourth power shows that sunspots emit less than half as much energy per square kilometer than their surroundings.

• If you could cut out a sunspot and set it aside, it would glow brightly. They appear dark only in contrast to their surroundings.

• The surface area of a sphere is

where R is the radius of the sphere.

• A spherical blackbody (e.g. a star) will produce a luminosity, L, of

= (surface area)(energy emitted per unit of surface area)

• Hot objects glow.

• The hotter the object the brighter the glow.

• The hotter the object the ``bluer" the emitted light.

Updated March 14, 2012