An air conditioner supplies cold air at the same temperature to each room on the fourth floor of the building shown in Fig. The floor plan is shown in Fig. The cold air flow produces an equal amount of heat flow ݍ out of each room. Write a set of differential equations governing the temperature in each room, where To= temperature outside the building, Ro= resistance to heat flow through the outer walls, Ri= resistance to heat flow through the inner walls. Thermal capacitance of each room is C. Assume that (1) all rooms are perfect squares, (2) there is no heat flow through the floors or ceilings, and (3) the temperature in each room is uniform throughout the room. Take advantage of symmetry to reduce the number of differential equations to three.

An air conditioner supplies cold air at the same temperature to each room on the fourth floor of the building shown
in Fig. The floor plan is shown in Fig. The cold air flow produces an equal amount of heat flow ݍ out of each room. Write a set of
differential equations governing the temperature in each room, where To= temperature outside the building, Ro= resistance to heat
flow through the outer walls, Ri= resistance to heat flow through the inner walls. Thermal capacitance of each room is C. Assume
that (1) all rooms are perfect squares, (2) there is no heat flow through the floors or ceilings, and (3) the temperature in each room
is uniform throughout the room. Take advantage of symmetry to reduce the number of differential equations to three.