4. Dry air at a constant container. The pressure at the inlet is pi temperature of T passes through a valve into a rigid spherical The linear resistances of the two valves at the inlet and the outlet are Ry and Rs, respectively. Assume that the process is isothermal. Denote the volume flow rate at the outlet as o (a) Develop a mathematical model of the pressure p in the container. (b) Determine the transfer function relating pi and p for this pncumatic system if 9o 5. As shown in the figure, the wall of a room consists of two layers, for which the thermal capacitances are Ci and C2. Assume that the temperatures in both layers are uniform and they are T, and T2 respectively. The temperatures inside and outside the room are Ti and To respectively. Both layers exchange heat by convection with air and the thermal resistances are Ri and R3, respectively. The thermal resistance of the interface between the layers is R2 (a) Derive the differential equations for this system. (b) Using the differential equations obtained in part (a), determine a state-space representation for the system. Assume the temperatures Ti and T2 are the outputs. GIG