Canonical thermostatics of ideal gas in the frame work of generalized uncertainty principle

The statistical consequences of minimal length supposition are investigated for a canonical ensemble of ideal gas. These effects are encoded in the so-called Generalized Uncertainty Principle (GUP) of the second order. In the frame work of the considered GUP scenario, a unique partition function is obtained by using of two different methods of quantum and classical approaches. It should be noticed that here we consider the magnitude of the momentum in the deformed Hamiltonian of the model. In this way the model is different from the already existing model which does not have any signicant result in quantum approach. In particular, the corrections to the thermodynamical characteristics such as the mean energy, the entropy and the density of states are achieved. The induced improvements manifest themselves at very high temperature limits. However it is shown that, if one apply the predicted observational bound on the GUP deformation parameter, the modications become more observable even at intermediate temperatures. The deformation parameter of the considered GUP model also estimated for nowadays precision of measurements of the heat capacity of an ensemble of hydrogen atoms.