On a warm summer day, you decide to leave a fan running in your room. The room is 12 ft x 15 ft x 8 ft. The room is full of dry air. When you leave the room, the air temperature is 75oF. The fan has a 0.10 hp motor. Assuming that the air pressure stays constant at 14.7 psia, and that the room is perfectly insulated, determine the air temperature in the room when you return in 8 hours.

Question

Given: Air; L = 12 ft; W = 15 ft; H = 8 ft; T1 = 75oF = 535 R; W?=?0.1 hp=?254.5 Btu/hr; P = 14.7 psia; t = 8 hours
Assume: Q = 0 (insulated); ?KE = ?PE = 0
Air behaves as an ideal gas with constant specific heats: cv = 0.172 Btu/lbm-R
R = 53.33 ft-lbf/lbm-R
P = constant
What will be an ideal response?

Answer 1

Solution: This is a closed system. Therefore, beginning with the First Law for closed systems, the First Law can be reduced to
W = m (u1 – u2)
In 8 hours, the total work is W = W?t = (-254.5 Btu/hr) (8 hr) = -2036 Btu

V = LWH = 1440 ft3
m = PV/RT1 = 106.8 lbm
W = m cv(T1 – T2)
Solving: T2 = 186oF
Fans “cool” by increasing convective heat transfer from people or things. In reality, they heat the air. Fortunately, rooms typically aren’t perfectly insulated. Also, any objects in the room must also warm, and this will reduce actual temperature increases for the air.