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A1. A vessel is used as a surge dampener (to reduce the size of pressure surges) for a gas stream. The molar flowrate of the gas into the vessel at time t is Min(t). The molar flowrate at time t out of the vessel is given by: Mout(t) = C/Pt) Here P(t) is the internal pressure of the vessel and C is a constant. The vessel has volume V, and the gas behaves as an ideal gas at constant temperature T. Develop a dynamic model of this system with the general form: dP*(t) + P*(t) = KMin(t) dt (c) At a given moment (at t = 0), the molar flowrate of gas entering the surge vessel increases by an amount, h. This higher flowrate persists for tw seconds, after which the inlet flowrate falls to its previous level. ttw The Laplace Transform of this function is: L{Min (t)} = (1 e-tws) h 1 - e) Find a function to express the change in gas pressure with time after this disruption to the inlet flowrate. You may make use of the following identities: L- "+ )] = 1- exp p(- Is(ts + 1) t