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Two perfect monoatomic gases at absolute temperatures $T_{1} and T_{2}$ are mixed. There is no loss of energy. The masses of the molecules are $m_{l} and m_{2}$ .The number of molecules in the gases are $n_{1} and n_{2}$ .The temperature of the mixture is

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$T_{1} + T_{2}$

$\frac{T_{1} + T_{2}}{2}$

$\frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}}$

$\frac{n_{1} T_{1} - n_{2} T_{2}}{n_{1} + n_{2}}$

answer is C.

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Detailed Solution

$\frac{3}{2} {kT}_{1} \times n_{1} + \frac{3}{2} {kT}_{2} \times n_{2} = (n_{1} + n_{2}) \frac{3}{2} kT$

or $T = \frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}}$

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