Alpha Geek
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A single-room building has four identical exterior walls, 5 m wide by 3 m high, with a perfectly insulated roof and floor. The thermal resistance of the walls is R = 4.5 × 10−3 K/W · m2. Taking the only significant thermal capacitance to be the room air, obtain the expression for the steady-state room air temperature if the outside air temperature varies sinusoidally about 15◦C with an amplitude of 5° and a period of 24 h. The specific heat and density of air at these conditions are cp = 1004 J/kg · K and ρ = 1.289 kg/m3.