A rigid steel tank of finite volume V is filled with compressed air and at t = 0 a valve is to be opened to allow the tank to discharge into the atmosphere. It is desired to predict the resulting tank pressure P(t), if the temperature remains constant at T₀.

(a) Assuming that w(t) = αP(t), where w is the mass flow rate out of the tank and α is a constant, determine P(t).

(b) For what range of P is the assumed proportionality between w and P likely to be a good approximation, and how then could you calculate α?