Surge drums are often used as intermediate storage capacity for gas streams that are transferred between chemical process units. Consider a surge drum of constant volume V = 100 L as shown in Figure 1, where qi and a denote the inlet and outlet molar flow rates respectively (mol/min). The surge drum is operating at a constant temperature T = 298 K. qi P a Figure 1 a) Develop a dynamic model that describes how the pressure (P) in the drum varies with time. State an assumption that you made. b) What is the state variable for the model in part (a)? c) Suppost that the outlet molar flow rate is given as: q = a(P-P) where a = 2 mol. s-1 atm-1 is the flow coefficient, Pa = 1 atm is the constant head pressure. Find the steady state relation between input (qis ) and output (Ps). Hence, sketch a graph for the steady state input-output relation. You are expected to denote the value of y-intercept. d) Consider the case when there is no inlet molar flow and the outlet flow rate is given as: q=B/P-PM where B = 0.1 mol. s -- atm is the flow coefficient, Pn = 1 atm is the constant head pressure. Given that initially, the pressure in the surge drum is at 5 atm. Obtain the pressure profile as a function of time. The ideal gas constant R = 0.08205 L.atm. mol-1.K-1 (Hint: You may use the method of substitution during integration.) e) Using the result in part (d), identify the minimum possible pressure in the gas surge drum, and calculate the time required to achieve this minimum pressure. 1) Sketch a graph of pressure P against time t and label important values for the x and y-axes on the graph