A) \[2{{P}_{a}}{{V}_{a}}={{P}_{b}}{{V}_{b}}\]
B) \[{{P}_{a}}\ne {{P}_{b}},{{V}_{a}}={{V}_{b}}\]
C) \[\frac{{{P}_{a}}}{{{V}_{a}}}=\frac{{{P}_{b}}}{{{V}_{b}}}\]
D) \[{{P}_{a}}{{V}_{a}}={{P}_{b}}{{P}_{v}}\]
Correct Answer: D
Solution :
When the gases are in thermal equilibrium, it means the temperature of the gases are same, therefore according to Boyles law \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\] Here: \[{{P}_{1}}={{P}_{a}}\] \[{{V}_{1}}={{V}_{a}}\] \[{{P}_{2}}=Pb\] \[{{V}_{2}}=Vb\] Hence, \[{{P}_{a}}{{V}_{a}}={{P}_{b}}{{V}_{b}}\]
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