A) \[{{T}_{1}}={{T}_{2}}\]
B) \[({{T}_{1}}+{{T}_{2}})/2\]
C) \[\frac{{{T}_{1}}{{T}_{2}}({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}})}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]
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 guiding principle in this problem is that the total number of moles of the system remain the same. |
\[\frac{{{P}_{1}}{{V}_{1}}}{R{{T}_{1}}}+\frac{{{P}_{2}}{{V}_{2}}}{R{{T}_{2}}}=\frac{P({{V}_{1}}+{{V}_{2}})}{RT}\] |
or \[T=\frac{P({{V}_{1}}+{{V}_{2}}){{T}_{1}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\] |
By Boyle's law, \[P({{V}_{1}}+{{V}_{2}})={{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}\] |
\[\therefore \] \[P=\frac{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}\] |
\[\therefore \] \[T=\frac{({{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}){{T}_{1}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\] |
You need to login to perform this action.
You will be redirected in
3 sec