A) \[{{T}_{1}}+{{T}_{2}}\]
B) \[({{T}_{1}}+{{T}_{2}})/2\]
C) \[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]
D) \[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\]
Correct Answer: C
Solution :
[c] The number of moles of the system remains same, |
\[\frac{{{P}_{1}}{{V}_{1}}}{R{{T}_{1}}}+\frac{{{P}_{2}}{{V}_{2}}}{R{{T}_{2}}}=\frac{P({{V}_{1}}+{{V}_{2}})}{RT}\] Þ \[T=\frac{P({{V}_{1}}+{{V}_{2}}){{T}_{1}}{{T}_{2}}}{({{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}})}\] |
According to Boyles law, |
\[{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}=P({{V}_{1}}+{{V}_{2}})\] \ \[T=\frac{({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}){{T}_{1}}{{T}_{2}}}{({{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}})}\] |
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