Specific Heat Of An Ideal Free-Particle Model In Three Dimensions With Intermediate Statistics At Low Temperature

The grand partition function of intermediate statistics with a standard method is derived to calculate the thermodynamic properties of an ideal free-particle model in three dimensions. The specific heat of the model at low temperature is discussed by taking the ground state energy and the occupation number into consideration. The results show that the properties of this model and the ideal fermion model are similar when m (the maximum occupation number in a single-particle state) is a smaller positive integer, and the specific heat decreases with the increase of m except for m being 2 or 3. When m is a bigger positive integer, the properties of the model are similar to that of an ideal boson model. A new statistics method -generalized intermediate statistics-is obtained, and it is applied to an ideal free-particle model in three dimensions. In this model, the particles in ground state are bosons and the particles in excited state are fermions. The thermodynamic properties and specific of the model are calculated. It shows that the model turns into the condensation at low temperature just like BEC. The changes in energy varied with the temperature of the model are more marked than those of an ideal boson model. In other words, the specific curve is blow on the curve of the boson model. As the higher critical temperature, the maximum of specific is about two time than that of the boson model. The specific curve is close to the classic limited Cv/Nk=3/2 when temperature rise.