When the next theory came forward in 1907

When considering gasses, they possess two types of heat capacities namely,the heat capacity at constant volume (CV) and the heat capacity at constant pressure (CP). But when considering the solids, both the heat capacities become almost equal to each other. Therefore only one capacity is defined for solids. Three theories have been put forward by various physicists to explain the heat capacity of solids. The first theory was “Dulong and Petit theory”. This was first explained in 1819 1. Here they assumed the atoms in a solid behave as classical harmonic oscillators. It was proved in this theory that the molar heat capacity of all solids is constant and is independent of temperature or frequency. Although this theory agreed with the experimented values at very high temperatures, at low temperatures it failed miserably. Therefore the next theory came forward in 1907 to explain the heat capacities of solids. This is known as the “Einstein Theory”. Einstein applied Planck?s idea of quantization to lattice vibrations.Here Einstein assumed that atoms in a lattice vibrate independently with the same angular frequency ?. This theory agreed with the experimental data at very high temperatures and at very low temperatures, but it showed disagreements at intermediate temperatures. The reason for the failure was the above assumption. Then later in 1912 an American-Dutch physicist Peter Debye introduced the Debye theory to explain the heat capacities of solids. Since atoms in a crystal are coupled together they can?t vibrate independently. They form coupled harmonic oscillators. Therefore atoms vibrate in a range of frequencies. These facts were taken in to account by Debye when proposing the Debye theory. He suggested that crystals can propagate elastic waves of wavelengths ranging from low frequencies through high frequencies. The highest frequency that can propagate through the crystal was named as the “Debye frequency” of the particular crystal. Debye theory agreed well with the experimental data of the heat capacities of solids. The Debye frequency depends on the number of atoms in the crystal, the volume of the considered specimen and the velocity of sound through the sample. The velocity of sound through the sample could be determined by determining the velocities of Longitudinal and the Transverse waves through the sample, which relates to the Young?s modulus and the Rigidity modulus of the particular sample.