Show a vertical cylindrical vesse seperated in two parts by a frictionless piston free to move along the length of vessel. The length of the cylilender is 90 cm and the piston divides the cylinder in the ratio of 5:4. Each of the two parts of the vessel contains 0.1 mole of an ideal gas. The temoerature of the gas is 300K in each part. Calculate the mass of the piston.(figure)

Explanation

`m`: mass of piston

For equilibrium of piston
`P_(1) + (m g)/(A) = P_(2)`
`m g = (P_(2) - P_(1))A` (i)
Chamber `①`, `P_(1)V = n_(1)R T rArr P_(1) = (n_(1) R T)/(V) = (n_(1) R T)/(A xx 0.5)`
Chamber `②`, `P_(2)V = n_(2)R T rArr P_(2) = (n_(2) R T)/(V) = (n_(2) R T)/(A xx 0.4)`
`(P_(2) - P_(1))A = ((n_(2) R T)/(0.4 A) - (n_(1) R T)/(0.5 A))A = 0.1 R T ((1)/(0.4) - (1)/(0.5))`
`= 0.1 R T (2.5 - 2) = 0.05 R T`
`mg = (P_(2) - P_(1))A = 0.05 R T`
`m = (0.05 R T)/(g) = (0.05 xx 8.3 xx 300)/(10)`
`= 12.45 kg`