Air is contained at a constant temperature within a vertical cylinder of height 100 cm . The top is sealed by a light, frictionless piston. Atmospheric pressure is equivalent to 75 cm of mercury. Mercury is slowly poured onto the piston. Determine the maximum height of the mercury column that can be placed on the piston.

Step-by-step solution

Let A be the cross-sectional area of the cylinder. Initial pressure of the enclosed air, P₁ = 75 cm of Hg. Initial volume of the air, V₁ = 100 A . Let x be the maximum height of the mercury column poured onto the piston. The final pressure of the air becomes P₂ = (75 + x) cm of Hg. At the maximum height of the mercury column, the total height of the air column and the mercury column will be exactly equal to the height of the cylinder. Thus, the final length of the air column is (100 - x) cm . Final volume of the ai