Question

1. A slide projector contains a 500 W light bulb that is cooled by an internal fan that blows room air across the bulb at a rate of 1.00 kg/min. If the equilibrium surface temperature of the bulb is 350 °C and the inlet temperature (the room air) is at 20.0 °C, then determine a) the outlet temperature of the cooling air and b) the rate of entropy production in the air passing through the projector. Assume the air is an ideal gas with constant specific heat and that it undergoes an aergonic process.

Answer 1

a)

T_Inlet = Inlet temperature = 20.0 ^oC

T_outlet = outlet temperature = ?

P = Power of the bulb = 500 W

m = Rate of air flowing = 1 kg/min = 1 kg /60 sec = 0.0167 kg/s

c = specific heat of air = 1005 J(kg-K)

Power of the bulb is given as

P = m c (T_outlet - T_Inlet )

500 = (0.0167) (1005) (T_outlet - 20)

T_outlet = 49.8 ^oC

b)

S_outlet = 1767 J/(kg-K)

Sinlet = 1668 J/(kg-K)

T = equilibrium temperature = 350 ^oC = 350 + 273 = 623 K

Rate of entropy is given as

Rate = m (S_outlet - Sinlet ) - (P/T)

Rate = (0.0167) (1767 - 1668 ) - (500/623)

Rate = 0.851