Thermodynamics

76 | Thermodynamics•Q outEXAMPLE 2–12Heating Effect of a FanRoom•W elect. inFanA room is initially at the outdoor temperature of 25°C. Now a large fanthat consumes 200 W of electricity when running is turned on (Fig. 2–49).The heat transfer rate between the room and the outdoor air is given asQ· UA(T i T o ) where U 6 W/m 2 · °C is the overall heat transfer coefficient,A 30 m 2 is the exposed surface area of the room, and T i and T o are theindoor and outdoor air temperatures, respectively. Determine the indoor airtemperature when steady operating conditions are established.FIGURE 2–49Schematic for Example 2–12.Solution A large fan is turned on and kept on in a room that looses heat tothe outdoors. The indoor air temperature is to be determined when steadyoperation is reached.Assumptions 1 Heat transfer through the floor is negligible. 2 There are noother energy interactions involved.Analysis The electricity consumed by the fan is energy input for the room,and thus the room gains energy at a rate of 200 W. As a result, the room airtemperature tends to rise. But as the room air temperature rises, the rate ofheat loss from the room increases until the rate of heat loss equals the electricpower consumption. At that point, the temperature of the room air, andthus the energy content of the room, remains constant, and the conservationof energy for the room becomesE # in E # out⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭⎫⎪⎪⎬⎪⎪⎭Rate of net energy transferby heat, work, and mass dE system > dt→0 1steady2Rate of change in internal, kinetic,potential, etc., energies 0S E # in E # outSubstituting,It givesW # elect,in Q # out UA 1T i T o 2200 W 16 W>m 2 # °C2130 m 2 21T i 25°C2T i 26.1°CTherefore, the room air temperature will remain constant after it reaches26.1°C.Discussion Note that a 200-W fan heats a room just like a 200-W resistanceheater. In the case of a fan, the motor converts part of the electricenergy it draws to mechanical energy in the form of a rotating shaft whilethe remaining part is dissipated as heat to the room air because of the motorinefficiency (no motor converts 100 percent of the electric energy it receivesto mechanical energy, although some large motors come close with a conversionefficiency of over 97 percent). Part of the mechanical energy of theshaft is converted to kinetic energy of air through the blades, which is thenconverted to thermal energy as air molecules slow down because of friction.At the end, the entire electric energy drawn by the fan motor is converted tothermal energy of air, which manifests itself as a rise in temperature.FIGURE 2–50Fluorescent lamps lighting a classroomas discussed in Example 2–13.© Vol. 24/PhotoDiscEXAMPLE 2–13Annual Lighting Cost of a ClassroomThe lighting needs of a classroom are met by 30 fluorescent lamps, eachconsuming 80 W of electricity (Fig. 2–50). The lights in the classroom arekept on for 12 hours a day and 250 days a year. For a unit electricity cost of