An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area `10cm^(2)` and weight 1kg.The vessel itself is kept in a big chamber containing air at atmospheric pressure 100kPa. The length of the gas column is 20cm.if the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the tempaerature to remain constant throughout the process.

Explanation

Given , `A = 10 cm^2 = (10^-3)(m^2), m = 1kg `
` p=100kPa = (10^5)Pa, l=20 cm`
` Case 1: External pressure exists `
` Case 2 : Internal pressure does not exists `
` (P_1)(V_1) = (P_2)(V_2)`
` ((10^5) + 1 xx 9.8 / (10^-3)) V = (1 xx 9.8/(10^-3)) xx V_1)`
` rArr ((10^5) + 9.8 xx (10^3)) A xx l`
` = 9.8 xx (10^3) xx A xx l' `
` rArr ((10^5) xx 2 xx (10^-1)+ 2 xx 9.8 xx (10^2))`
` = 9.8 xx (10^3)l' `
` rArr l'= (2 xx (10^4) + 19.6 xx (10^2)/ 9.8 xx (10^3))`
= 2.24081 m .