A) \[\frac{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}\]
B) \[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\]
C) \[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]
D) \[\frac{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}\]
Correct Answer: C
Solution :
Internal energy of the system will remain conserved. \[\left( {{n}_{1}}+{{n}_{2}} \right){{C}_{v}}T={{n}_{1}}{{C}_{V}}{{T}_{1}}+{{n}_{2}}{{C}_{V}}.\,{{T}_{2}}\] \[\left( \frac{{{P}_{1}}{{V}_{1}}}{R{{T}_{1}}}+\frac{{{P}_{2}}{{V}_{2}}}{R{{T}_{2}}} \right)T=\frac{{{P}_{1}}{{V}_{1}}}{R}+\frac{{{P}_{2}}{{V}_{1}}}{R}+\frac{{{P}_{2}}{{V}_{2}}}{R}\,\,;\]\[T=\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]You need to login to perform this action.
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