Thermal Physics

Step 1: State Wien's Displacement Law. Wien's law states that the wavelength at which a black body emits the maximum amount of radiation, , is inversely proportional to its absolute temperature . where is Wien's displacement constant ( m⋅K).

Step 2: Set up a ratio for the two bodies P and Q. Since is constant for any black body:

Step 3: Rearrange the formula to solve for the unknown temperature, .

Step 4: Substitute the given values and calculate . - K - nm - nm Note that since we are using a ratio, we do not need to convert nanometers to meters.

Step 1: State the Stefan-Boltzmann Law. The law states that the total energy radiated per unit surface area of a black body per unit time (the radiant emittance or power, P) is directly proportional to the fourth power of the black body's absolute temperature . For a given object, and are constants, so .

Step 2: Set up a ratio for the two different temperatures. Let be the power emitted at temperature , and be the power emitted at .

Step 3: Substitute the given values and solve for . - W - K - K The ratio of temperatures is .

• Stefan-Boltzmann Law relates total energy to .
• Planck’s Law gives full radiation distribution.
• Kirchhoff’s Law relates emission and absorption.