A container having base area `A_(0)`. Contains mercury upto a height `l_(0)`. At its bottom a thin tube of length `4l_(0)` and cross-section area `A(AltltA_(0)`) having lower end closed is attached . Initially the length of mercury in tube is `3l_(0)`. in reamining part `2` mole of a gas at temperature `T` is closed as shown in figure . Determine the work done (in joule) by gas if all mercury is displaced from tube by heating slowly the gas in the rear end of the tube by means of a heater. (Given : density of mercury = `rho`, atmospheric pressure `P_(0) = 2l_(0)rhog, C_(v)` of gas = `3//2 R, A = (3//rho)m^(2), l_(0) = (1//9)`m , all units is `S.I.`)

Answer

5

Explanation

If x is length of mercury in tube then pressure of gas
`P' =P_(0) +rhogl_(0) + rhogx = 3rhogl_(0) + rhogx implies W= - int_(3//0)^(0) (3rhogl_(0) + rhogx) Adx = 13.5 rhogAl_(0)^(2) = 5`