Find the final temperature of a mixture of two gases. If one gas has pressure \(P_1\), temperature \(T_1\), number of moles \(n_1\) and volume \(V_1\); and the second gas has pressure \(P_2\), temperature \(T_2\), number of moles \(n_2\) and volume \(V_2\). If the final pressure is \(P\) and final volume is \(V\), find the final temperature of the mixture.