A) \[{{P}_{A}}{{V}_{A}}={{P}_{B}}{{V}_{B}}\]
B) \[{{P}_{A}}={{P}_{B}},\,\,{{V}_{A}}\ne {{V}_{B}}\]
C) \[{{P}_{A}}={{P}_{B}},\,\,{{V}_{A}}={{V}_{B}}\]
D) \[\frac{{{P}_{A}}}{{{V}_{A}}}=\,\,\frac{{{P}_{B}}}{{{V}_{B}}}\]
Correct Answer: B
Solution :
According to problem mass of gases are equal so number of moles will not be equal i.e. \[{{\mu }_{A}}\ne {{\mu }_{B}}\] From ideal gas equation \[\operatorname{PV}=\,\mu RT\Rightarrow \frac{{{P}_{A}}{{V}_{A}}}{{{\mu }_{A}}}=\frac{{{P}_{B}}{{V}_{B}}}{{{\mu }_{B}}}\] [As temperature of the container are equal] From the relation it is clear that if \[{{\operatorname{P}}_{A}}={{P}_{B}}\] then \[\frac{{{V}_{A}}}{{{V}_{B}}}\,\,=\,\,\frac{{{\mu }_{A}}}{{{\mu }_{B}}}\ne 1\,\,\,i.e.\,\,{{V}_{A}}\ne {{V}_{B}}\] Similarly if \[{{V}_{A}}={{V}_{B}}\] then \[\frac{{{P}_{A}}}{{{P}_{B}}}=\frac{{{\mu }_{A}}}{{{\mu }_{B}}}\ne 1\] i.e. \[{{P}_{A}}\ne {{P}_{B}}\]
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