Room air at 23oC is heated by a 2000 W space heater with a surface filament temperature of 800 K. The room, at steady state, looses the power to the outside, which is at 7oC. Find the rate (s) of entropy generation and specify where it is made. Set up control volumes around the heater, the space between heater and the room wall (the air), and the wall between the inside and outside.

S (filament) = 2.5 W/K, S (heater/room) = - 9.257 W/K, S (air/outside) = 0.386 W/K

Explanation:

Room air temperature T (l) = 296K

Filament Temperature T₂ = 800 K

Heat pump, Q = - 2000W

Outside Temperature, T₃ = 7° C = 280 K

Use the relation of entropy to heat to find out the entropy generation at each interface

[S (generated) (1 to 2) ]filament = - ∫dQ/T

At filament

S = - (-2000) / 800

S = 2000/800 = 2.5 W/K

At the space between the heater and the room

S (heater to room) = - ∫dQ/T

S (heater to room) = (-2000/800) - (2000/296)

S (heater to room) = - 9.257W/K

At wall between air and outside

S (air to outside) = - ∫dQ/T

S (air to outside) = (-2000/296) + (2000/280)

S (air to outside) = 0.386 W/K