Q. Three perfect gases at absolute temperature $T_{1},\ T_{2}\ and\ T_{3}$ 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) $\frac{n_{1}{T_{1}}^{2} + n_{2}{T_{2}}^{2} + n_{3}{T_{3}}^{2}}{n_{1}T_{1} + n_{2}T_{2} + n_{3}T_{3}}$
C) $\frac{{n_{1}}^{2}{T_{1}}^{2} + {n_{2}}^{2}{T_{2}}^{2} + {n_{3}}^{2}{T_{3}}^{2}}{n_{1}T_{1} + n_{2}T_{2} + n_{3}T_{3}}$
D) $\frac{T_{1} + T_{2} + T_{3}}{3}$
Explanation
(a) $\frac{F}{2}n_{1}kT_{1} + \frac{F}{2}n_{2}kT_{2} + \frac{F}{2}n_{3}kT_{3}$
=$\frac{F}{2}\left( n_{1} + n_{2} + n_{3} \right)kT$
$T = \frac{n_{1}T_{1} + n_{2}T_{2} + n_{3}T_{3}}{n_{1} + n_{2} + n_{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.