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 - Physics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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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 $\frac{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}{n _{1} + n _{2} + n _{3}}$
B $\frac{n _{1}^{2} T _{1} + n _{2}^{2} T _{2} + n _{3}^{2} T _{3}}{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}$
C $\frac{n _{1} T _{1}^{2} + n _{2} T _{2}^{2} + n _{3} T _{3}^{2}}{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}$
D $\frac{T _{1} + T _{2} + T _{3}}{3}$

Solution & Step-by-step Explanation

Total internal energy is conserved: U = U_{1} + U_{2} + U_{3} .For monatomic gases: \frac{3}{2} (n_{1} + n_{2} + n_{3}) k T = \frac{3}{2} n_{1} k T_{1} + \frac{3}{2} n_{2} k T_{2} + \frac{3}{2} n_{3} k T_{3} . T = \frac{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}{n _{1} + n _{2} + n _{3}} The result is independent of the masses of the individual molecules.

Try it yourself before checking the explanation above.

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:

\frac{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}{n _{1} + n _{2} + n _{3}}

\frac{n _{1}^{2} T _{1} + n _{2}^{2} T _{2} + n _{3}^{2} T _{3}}{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}

\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}}

\frac{T _{1} + T _{2} + T _{3}}{3}

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