A) \[\frac{{{P}_{1}}}{{{T}_{1}}}+\frac{{{P}_{2}}}{{{T}_{2}}}\]
B) \[\frac{{{P}_{1}}{{T}_{1}}+{{P}_{2}}{{T}_{2}}}{{{({{T}_{1}}+{{T}_{2}})}^{2}}}\]
C) \[\frac{{{P}_{1}}{{T}_{2}}+{{P}_{2}}{{T}_{1}}}{{{({{T}_{1}}+{{T}_{2}})}^{2}}}\]
D) \[\frac{{{P}_{1}}}{2{{T}_{1}}}+\frac{{{P}_{2}}}{2{{T}_{2}}}\]
Correct Answer: D
Solution :
From ideal gas equation, \[pV=\mu RT\] \[\therefore \] \[\mu =\frac{pV}{RT}\] \[\therefore \] Number of moles of gas in first container, \[{{\mu }_{1}}=\frac{{{p}_{1}}V}{R{{T}_{1}}}\] Number of moles of gas in second container, \[{{\mu }_{2}}=\frac{{{p}_{2}}V}{R{{T}_{2}}}\] Number of moles in containers when joined with each other, \[\mu =\frac{pV}{RT}\] But, \[\mu ={{\mu }_{1}}+{{\mu }_{2}}\] \[\frac{p(2V)}{RT}=\frac{{{p}_{1}}V}{R{{T}_{1}}}=\frac{{{p}_{2}}V}{R{{T}_{2}}}\] \[\frac{2p}{T}=\frac{{{p}_{1}}}{{{T}_{1}}}+\frac{{{p}_{2}}}{{{T}_{2}}}\] \[\frac{P}{T}=\frac{{{p}_{1}}}{2{{T}_{1}}}+\frac{{{p}_{2}}}{2{{T}_{2}}}\]
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