Analysis

The analysis of these results proceeds in four steps.

1. First we connect our observations of with a basic property of the radiation inside of the cavity, , the energy per unit volume at a temperature T inside the interval . (Here again, we are wearing the ``filter glasses'' when looking at the experiment.)

2. Next, we break the energy density into a part depending on the cavity, the number of modes in the frequency interval (), and a part depending on the properties of radiation, the average energy per mode in the frequency interval at temperature T, .

3. We then count the number of modes in the interval .

4. We then determine and try to understand the average energy per mode,

The remaining subsections within this section follow this program.

• Connecting with
• Counting the modes
  • : How many modes have frequency less than ?
  • : How many modes/volume in the interval .
• : the average energy per mode.
  • The average energy of a two-level system
  • The average energy of a ``continuous'' electromagnetic mode
  • The average energy of a ``continuous'' electromagnetic mode
  • The average energy under Planck's Hypothesis