An inequality by P'olya establishes that the product between the torsional rigidity and the first Dirichlet Laplacian eigenvalue is bounded from above in the class of bounded sets with given measure. We investigate the sharpness of the constant appearing in P'olya's inequality and we try to improve it in a suitable class of sets. This is a joint work with M. van den Berg, V. Ferone and C. Nitsch.