Solution Found!
A single-room building has four identical exterior walls,
Chapter , Problem 9.4(choose chapter or problem)
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 \(R=4.5 \times 10^{-3} \mathrm{~K} / \mathrm{W} \cdot \mathrm{m}^{2}\). 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 \(15^{\circ} \mathrm{C}\) with an amplitude of \(5^{\circ}\) and a period of 24 h. The specific heat and density of air at these conditions are \(c_{p}=1004 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) and \(\rho=1.289 \mathrm{~kg} / \mathrm{m}^{3}\).
Questions & Answers
QUESTION:
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 \(R=4.5 \times 10^{-3} \mathrm{~K} / \mathrm{W} \cdot \mathrm{m}^{2}\). 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 \(15^{\circ} \mathrm{C}\) with an amplitude of \(5^{\circ}\) and a period of 24 h. The specific heat and density of air at these conditions are \(c_{p}=1004 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) and \(\rho=1.289 \mathrm{~kg} / \mathrm{m}^{3}\).
ANSWER:Step 1 of 5
The following are given from the question:
The width of the wall of room, \(w=5 \mathrm{~m}\)
The height of the wall of room, \(h=3 \mathrm{~m}\)
The length of the wall of room, \(I=4 \mathrm{~m}\)
The thermal resistance of wall, \(R=4.5 \times 10^{-3} \frac{\mathrm{K}}{\mathrm{Wm}^{2}}\)
Air heat capacity, \(c_{p}=1004 \frac{\mathrm{J}}{\mathrm{kg}}\)
Air density, \(\rho=1.289 \frac{\mathrm{kg}}{\mathrm{m}^{3}}\)
The steady state room air temperature, \(T=15^{\circ} \mathrm{C}\)
The amplitude at \(15^{\circ} \mathrm{C}\) for the period of \(24 \mathrm{hr}\), \(A_{T}=5^{\circ}\)