Two identical rooms as sketched in figure are heated

Question

Question: Two identical rooms (as sketched in Figure) are heated differently during wintertime by means of two heat sources of known heat flow rates q₁ and q₂. The

rooms have identical walls separating the conditioned space from the outside. Heat also flows through the wall separating the two rooms, which is different from the outside walls. Knowing the outside temperature is i_o, derive the mathematical model of this thermal system where the output amounts are the two room temperatures i₁ and i₂. Known are the thermal resistances of the outside walls R_th,o, the thermal resistance of the separating wall R_th, and the thermal capacitances of the two rooms Cth, as well as the outdoor temperature io and the two source heat flow rates q₁ and q₂.