  We present an exact treatment of the thermodynamics of physical systems in
the framework of the generalized uncertainty principle (GUP). Our purpose is to
study and compare the consequences of two GUPs that one implies a minimal
length while the other predicts a minimal length and a maximal momentum. Using
a semiclassical method, we exactly calculate the modified internal energies and
heat capacities in the presence of generalized commutation relations. We show
that the total shift in these quantities only depends on the deformed algebra
not on the system under study. Finally, the modified internal energy for an
specific physical system such as ideal gas is obtained in the framework of two
different GUPs.
