Transient AnalysisThe air supply to a 2000-ft3 office has

QUESTION:

The air supply to a \(2000-\mathrm{ft}^{3}\) office has been shut off overnight to conserve utilities, and the room temperature has dropped to \(40^{\circ} \mathrm{F}\). In the morning, a worker resets the thermostat to \(70^{\circ} \mathrm{F}\), and \(200 \mathrm{ft}^{3} / \mathrm{min}\) of air at \(120^{\circ} \mathrm{F}\) begins to flow in through a supply duct. The air is well mixed within the room, and an equal mass flow of air at room temperature is withdrawn through a return duct. The air pressure is nearly 1 atm everywhere. Ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach \(70^{\circ} \mathrm{F}\). Plot the room temperature as a function of time.