Motivated by recent experiments on phase behavior of systems confined in porous media, we have studied the effect of quenched bond randomness on the nature of the phase transition in the two dimensional Potts model. To model the effects of the porous matrix we chose the couplings of the q state Potts Hamiltonian from the distribution P(J
) = pδ(J
– J) + (1 – p)δ(J
). For a range of p values, away from the percolation threshold, the transition temperature follows the mean field prediction T
(p) = Tc(1)p. Furthermore, we observed that the strong first order transition, that appears in the pure case for q = 10, changes two a second order transition. It is also clear from our simulations that the second order transition of the q = 3 pure case changes to a second order transition of a different universality class. A finite size scaling analysis suggests that in both cases the critical exponents, in the presence of disorder, fall into the universality class of the two dimensional pure Ising model. This result agrees with theoretical calculations recently published .