During steady-state operation, a parallel –shaft transmission receives 600 kw through the high-speed shaft, but owing to friction and other irreversibilities, delivers 588 kw through the low-speed shaft. the transmission is cooled on its outer surface according to:

q = -ha(ttrans – t.)

where h is the heat transfer coefficient, a is the outer surface area, ttrans is the uniform temperature of the outer surface of the transmission and to is the uniform temperature of the surroundings away from the immediate vicinity of the gearbox.

evaluate the rate of entropy production for :

(a) the gearbox system
(b) an enlarged system consisting of the gearbox and enough of its surroundings that the heat transfer occurs at t0.

let h=0.17 kw/m2-k, a=1.8 m2 and t0=239 k.