At the beginning of the 20th century Quantum Mechanical theory was established after the collapse of classical mechanics. It starts with the discovery of electromagnetic energy quantization by Max Planck needed to explain black body radiation distribution as a function of frequency and temperature. He explained it by a model where resonators can emit radiation only by quanta of energy. Later Bohr predicted the Quantum Mechanical model for the Hydrogen atom, using Planck’s constant as a measure for angular momentum quantization1. An important concept in his work was the correspondence principle. According to this principle the quantum mechanical results should coincide with classical calculation at large quantum numbers. Planck came up with a resolution, which involved the idea of light as a wave phenomenon described by Maxwell’s equation. Einstein used the developing quantum mechanical theory to explain Planck distribution function by investigating the processes of emission and absorption of light by a simple system.
Black body radiation is important when studying electromagnetic radiation and thermal radiation. A black body refers to an object that emits thermal radiation. Overall a black body is one that absorbs all incoming light and does not reflect any. An object tended to appear black at room temperature however as temperature increased a black body began to emit thermal radiation. Planck and other physicist discovered that as the temperature of a black body increases the total amount of light emitted per second increases and the wavelength of the spectrum’s peak shifts towards blue wavelength. (See figure below). http://library.thinkquest.org/C007571/english/advance/background4.htm

Overall black body radiation can be described mathematically with Planck’s Radiation Law, which displays the intensity of radiation from the black body as a function of wavelength for a fixed temperature. Planck’s law can be seen below in figure 1.

Fig. 1

However Planck’s law was derived from Wein Displacement Law and Steffan-Boltzman Law. Overall Wein Displacement Law explains the wavelength of the peak of the distribution and Steffan-Boltzman Law explains the total energy being emitted. Both laws can be seen below in figure 2.

Fig. 2

Figure 2 displays the two laws responsible for the derivation of Planck’s Law. Both equations where used in Planck’s law as seen in figure 1. However Planck continued to explore the idea of how molecules in these black bodies exchanged energy. Thus the concept of entropy was derived. Entropy is measured by the amount of heat that can be transformed into energy, and varies inversely with the temperature of the body. The equation that represents entropy can be seen below.

Fig. 3 Where k is the Boltzman constant and omega is the volume of the macrostate. Planck was responsible for the derivation of the above equation. Entropy is the measure of the probability of a given macrostate. The second law of thermodynamics describes how the entropy of a system changes with time.