Question

- solid state - what is mean in low tempreture , spesific heat change with T^3 ? hint , think about phonone

Answer 1

The low temperature specific heat of solid crystal is described by Debye model, where the heat capacity is proportional to T3. Before Debye, Einstein proposed a model of heat capacity at low temperature where he considered only one type of mode of vibration exists within the crystal lattice that contributes to the lattice heat capacity. This mode is known as Optical mode.  This model assumed that the energy of optical mode is quantized and no dependence on momentum space. The heat capacity will drop exponentially will at low temperature. Though it failed to describe the heat capacity T3 at low temperature.

Latter Debye proposed his model of heat capacity where he considered that the atoms are assumed to oscillate both with their own frequencies and modes. So you won’t be able to assume a constant density of states (which are called Phonons) as in the case of the Einstein model. Where the specific heat capacity Cv = (T/θD) at low temperature limit [T<θD ][θD = Debye temperature] and well explained the experimental data.