For the three-room house shown in Figure 7.35, all rooms are perfect squares and have the same dimensions. An air conditioner produces an equal amount of heat flow \(q_{\mathrm{ho}}\) out of each room. The temperature outside the house is \(T_{\mathrm{o}}\). Assume that there is no heat flow through the floors or ceilings. The thermal resistances through the inner walls and the outer walls are \(R_{\mathrm{i}}\) and \(R_{\mathrm{o}}\), respectively. The thermal capacitance of each room is \(C\). Derive the differential equations for this system.

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FIGURE 7.35 Problem 6. Top view Ro The To R R