Final answer:
The common pressure reached when two gas chambers at different pressures are combined at constant temperature is the sum of the initial pressures, assuming no change in volume.
Step-by-step explanation:
The common pressure reached when two chambers containing m₁ gram and m₂ gram of a gas at pressures P₁ and P₂ respectively are put in communication with each other, with the temperature remaining constant, can be found using the principles of the ideal gas law. According to the ideal gas law, at constant temperature, the total pressure of a mixture of gases is the sum of the pressures that each would exert if it were alone in the container (partial pressures). When the gases are mixed, the volume remains constant, so the final common pressure would be the sum of P₁ and P₂, provided the container volume doesn't change.
For example, if P₁ = 300 mm Hg and P₂ = 500 mm Hg in equal-sized containers, the total pressure when these containers are combined into the same container is simply Ptotal = P₁ + P₂ = 300 mm Hg + 500 mm Hg = 800 mm Hg.