Three perfect gases at absolute temperature T1 , T2 and T3 are mixed. The masses of molecules are m1 , m2 and m3 and the number of molecules are n1 , n2 and n3 respectively….

Q: Three perfect gases at absolute temperature T1 , T2 and T3 are mixed. The masses of molecules are m1 , m2 and m3 and the number of molecules are n1 , n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is

(a) $\displaystyle \frac{T_1 + T_2 + T_3}{3}$

(b) $\displaystyle \frac{n_1 T_1 + n_2 T_2 + n_3 T_3}{n_1 + n_2 + n_3}$

(c) $\displaystyle \frac{n_1 T_1^2 + n_2 T_2^2 + n_3 T_3^2}{n_1 T_1 + n_2 T_2 + n_3 T_3}$

(d) $\displaystyle \frac{n_1^2 T_1^2 + n_2^2 T_2^2 + n_3^2 T_3^2}{n_1 T_1 + n_2 T_2 + n_3 T_3}$

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Ans: (b)