Two perfect gases having masses $m_{1}$ and $m_{2}$ at temperatures $T_{1}$ and $T_{2}$ are mixed
without any loss of internal kinetic energy of the molecules. The molecular weights
of the gases are $M_{1}$ and $M_{2}$ . What is the final temperature of the mixture ?

\frac{\frac{M_{1}}{M_{2}} T_{1} + \frac{M_{2}}{m_{2}} T_{2}}{\frac{M_{1}}{m_{1}} + \frac{M_{2}}{m_{2}}}

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\frac{\frac{m_{1}}{M_{1}} T_{1} + \frac{m_{2}}{M_{2}} T_{2}}{\frac{m_{1}}{M_{1}} + \frac{m_{2}}{M_{2}}}

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

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

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Solution

The correct option is B $\frac{\frac{m_{1}}{M_{1}} T_{1} + \frac{m_{2}}{M_{2}} T_{2}}{\frac{m_{1}}{M_{1}} + \frac{m_{2}}{M_{2}}}$
$U = U_{1} + U_{2}$

$∴ (n_{1} + n_{2}) \frac{1}{2} f k T = n_{1} \frac{1}{2} f k T_{1} + n_{2} \frac{1}{2} f k T_{2}$

$\Rightarrow T = \frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}} = \frac{\frac{m_{1}}{M_{1}} T_{1} + \frac{m_{2}}{M_{2}} T_{2}}{\frac{m_{1}}{M_{1}} + \frac{m_{2}}{M_{2}}}$

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Two perfect gases having masses m1 and m2 at temperatures T1 and T2 are mixedwithout any loss of internal kinetic energy of the molecules. The molecular weightsof the gases are M1 and M2. What is the final temperature of the mixture ?

The correct option is B m1M1T1+m2M2T2m1M1+m2M2U=U1+U2∴(n1+n2)12fkT=n112fkT1+n212fkT2⇒T=n1T1+n2T2n1+n2=m1M1T1+m2M2T2m1M1+m2M2

Two perfect gases having masses $m_{1}$ and $m_{2}$ at temperatures $T_{1}$ and $T_{2}$ are mixed
without any loss of internal kinetic energy of the molecules. The molecular weights
of the gases are $M_{1}$ and $M_{2}$ . What is the final temperature of the mixture ?