3rd year undergraduate at IIT Madras, IIT JEE Physics Tutor
Let 'd' be the density of air and 'n' be the ratio of specific heats.
1. Speed of sound = sq.rt(n*R*T)
2. For speed of adiabatic exhaust jet, we use Bernoulli's principle (assuming reversible discharge of gas) and Equation of state for the gas (P = d*R*T)
According to Bernoulli's principle, P1 + 0.5*d*v1*v1 = P2 + 0.5*d*v2*v2 Now, P1 = P (Pressure of gas in vessel) v1 = 0 (Since gas is practically stagnant) P2 = 0 (Since discharges to vacuum) v2 to be found out using the equation.
On making the above substitution and using State equation for P, we arrive at v2 = sq.rt(2*R*T)
Therefore the required ratio is v1/v2 = sq.rt(n/2)