2. Two identical rooms are designed, as sketched in the figure, with the six identical external walls. A cooling system operates in only one of the rooms. Consider it is summer time and heat flow infiltrates from the outside. Heat also flows through the wall separating the two rooms. Rith, 401 Rth,0 962 Rithio Rino 2 901 9 902 9 Cooler Ren Cth Cth RO 401 Ritno 902 a) Knowing the following amounts; heat flow absorbed by the cooler qi, the outside temperature T, as well as the walls thermal resistances and the two rooms thermal capacitances, find the mathematical model of this thermal system that expresses the two indoor temperatures T and T2. b) Obtain a state-space representation for the system with state variables T, and T2, input variables T, and qi, and output variables T, and T2