Kinetic Theory

JEE Main level, single correct, medium

20 of 168

Question 20 of 168

Three perfect gases at absolute temperatures T1,T2T_1, T_2 and T3T_3 are mixed. The masses of molecules are m1m_1, m2m_2 and m3m_3 and the number of molecules are n1,n2n_1, n_2 and n3n_3 respectively. Assuming no loss of energy, the final temperature of the mixture is :

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Answer: (A) n1T1+n2T2+n3T3n1+n2+n3\frac{n_1 T_1+n_2 T_2+n_3 T_3}{n_1+n_2+n_3}

Data ⇒n,k,t1+n2kT2+n3kT3=(n1+n2+n3)kT\Rightarrow n, k, t_1+n_2 k T_2+n_3 k T_3=\left(n_1+n_2+n_3\right) k T
∴T=n1T1+n2T2+n3T3n1+n2+n3\therefore T=\frac{n_1 T_1+n_2 T_2+n_3 T_3}{n_1+n_2+n_3}

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