EXAMPLE 2–12 Heating Effect of a Fan

A room is initially at the outdoor temperature of 25°C. Now a large fan

that 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 as

Q

·


UA(TiTo) 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 Tiand Toare the

indoor and outdoor air temperatures, respectively. Determine the indoor air

temperature when steady operating conditions are established.

Solution A large fan is turned on and kept on in a room that looses heat to

the outdoors. The indoor air temperature is to be determined when steady

operation is reached.

Assumptions 1 Heat transfer through the floor is negligible. 2 There are no

other 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 air

temperature tends to rise. But as the room air temperature rises, the rate of

heat loss from the room increases until the rate of heat loss equals the elec-

tric power consumption. At that point, the temperature of the room air, and

thus the energy content of the room, remains constant, and the conservation

of energy for the room becomes

Rate of net energy transfer Rate of change in internal, kinetic,

by heat, work, and mass potential, etc., energies

Substituting,

It gives

Therefore, the room air temperature will remain constant after it reaches

26.1°C.

Discussion Note that a 200-W fan heats a room just like a 200-W resis-

tance heater. In the case of a fan, the motor converts part of the electric

energy it draws to mechanical energy in the form of a rotating shaft while

the remaining part is dissipated as heat to the room air because of the motor

inefficiency (no motor converts 100 percent of the electric energy it receives

to mechanical energy, although some large motors come close with a conver-

sion efficiency of over 97 percent). Part of the mechanical energy of the

shaft is converted to kinetic energy of air through the blades, which is then

converted 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 to

thermal energy of air, which manifests itself as a rise in temperature.

EXAMPLE 2–13 Annual Lighting Cost of a Classroom

The lighting needs of a classroom are met by 30 fluorescent lamps, each

consuming 80 W of electricity (Fig. 2–50). The lights in the classroom are

kept on for 12 hours a day and 250 days a year. For a unit electricity cost of

Ti
26.1°C

200 W
1 6 W>m^2 #°C 21 30 m^221 Ti25°C 2

W

#

elect,in
Q

#

out
UA^1 TiTo^2

E

#

inE

#

out^ 
^ dEsystem^ >^ dt

0 1 steady (^2)
0 S E#
in
E

out
76 | Thermodynamics
Fan
Room
Qout
Welect. in

FIGURE 2–49

Schematic for Example 2–12.

FIGURE 2–50

Fluorescent lamps lighting a classroom
as discussed in Example 2–13.

© Vol. 24/PhotoDisc

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