  In this work we study a completely degenerated fermion gas at zero
temperature within a semiclassical approximation for the Hamiltonian arising in
polymer quantum mechanics. Polymer quantum systems are quantum mechanical
models quantized in a similar way as in loop quantum gravity that allow the
study of the discreteness of space and other features of the loop quantization
in a simplified way. We obtain the polymer modified thermodynamical properties
noticing that the corresponding Fermi energy is exactly the same as if one
directly polymerizes the momentum $p_F$. We also obtain the corresponding
expansion of thermodynamical variables for small values of the polymer length
scale $\lambda$. With this results we study a simple model of a compact object
where the gravitational collapse is supported by electron degeneracy pressure.
We find polymer corrections to the mass of the star. When compared with typical
measurements of the mass of white dwarfs we obtain a bound on the polymer
length of $\lambda^2\lesssim 10^{-26}m^2$.
