Question

Two gases of equal masses are in thermal equilibrium. If $ {{P}_{a}},{{P}_{b}} $ and $ {{V}_{a}},{{V}_{b}} $ are their respective pressures and volumes, then which relation is true?

• 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}} $

Answer 1

Answer: (D)

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}} $