A vertical cylinder fitted with a weighted leakproof piston

A vertical cylinder fitted with a weighted leak-proof piston with diameter 84.0 mm contains liquid H2O in thermodynamic equilibrium with the surrounding atmosphere, which is at 101.4 kPa and 102.8 degrees celcius. Determine the minimum mass on the piston in kg, to three significant figures. Use gravitational constant g = 9.81 m/s².

Solution

Force exerted by air on piston + Force due to weight = 101.4 x 1000 x (pi) x d² / 4

[ 101325 x (pi) x d² / 4 ]+ mg =101.4 x 1000 x (pi) x d² / 4

mg = 75 x (pi) x 0.084² / 4

m = 0.04236 kg = 42.368 gram