Three perfect gases at absolute temperatures $$T_1, T_2$$ and $$T_3$$ 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:

A

$$\dfrac{n_1 T_1 + n_2 T_2 + n_3 T_3}{n_1 + n_2 + n_3}$$

B

$$\dfrac{n_1 T_1^2 + n_2 T_2^2 + n_3 T_3^2}{n_1 T_1 + n_2 T_2 + n_3 T_3}$$

C

$$\dfrac{n_1^2 T_1^2 + n_2^2 T_2^2 + n_3^2 T_3^2}{n_1 T_1 + n_2 T_2 + n_3 T_3}$$

D

$$\dfrac{(T_1 + T_2 + T_3)}{3}$$