question_answer

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 [AIEEE 2011]

A) \[\frac{n_{1}^{2}T_{1}^{2}+n_{2}^{2}T_{2}^{2}+n_{3}^{2}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\]           

B)  \[\frac{{{T}_{1}}+{{T}_{2}}+{{T}_{3}}}{3}\]

C)  \[\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}\]

D)      \[\frac{{{n}_{1}}T_{1}^{2}+{{n}_{2}}T_{2}^{2}+{{n}_{3}}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}\]

Correct Answer: C

Solution :

[c]