A cylindrical container has insulating wall and an insulating piston which can freely move up and down without any friction. It contains a mixture of ideal gases. Originally the gas is at atmospheric pressure `P_(0)` and temperature `(T_(0))`. A tap positioned above the container is opened and it supplies water at a constant rate of `(dm)/(dt)= 0.25 kg//s`. The water collects above the piston in the container and the gas compresses. The tap is kept open till the temperature of the gas is doubled. During the process the T vs `(1)/(V)` graph for the gas was recorded and found to be a parabola with its vertex at origin as shown in the graph. Area of piston `A = 1.515 xx 10^(-3) m^(2)` and atmospheric pressure `= 10^(5) N//m^(2)`
(a) Find the ratio of `V_(rms)` and speed of sound in the gaseous mixture.
(b) For how much time the tap was kept open?

Answer

(a) `sqrt(2)` (b) 290 second