Three perfect gases at absolute temperature $T_1, T_2, T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is :

Question

( A ) $T = \frac{n_1T_1 + n_2T_2 + n_3T_3}{n_1 + n_2 + n_3} $
( B ) $\frac{n_1T_1 + n_2T_2^2 + n_3T_3^2}{n_1T_1 + n_2T_2+n_3T_3}$
( C ) $\frac{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2}{n_1T_1 + n_2T_2+n_3T_3}$
( D ) $\frac{(T_1 + T_2 + T_3)}{3}$