At steady state, the input shaft of a gearbox rotates at 2000 rpm while transmit

Question

At steady state, the input shaft of a gearbox rotates at 2000 rpm while transmitting a torque of 0.2 kNm. Due to friction, 1 kW of power is dissipated into heat and the rest is delivered to the output shaft. If the atmospheric temperature is 300 K and the surface of the gearbox maintains a constant temperature of 350 K, determine (a) the rate of entropy transfer into the atmosphere, (b) the rate of entropy generation in the system's universe, (c) the rate of entropy generation within the gearbox and (d) the rate of entropy generation in the immediate surroundings.

Explanation / Answer

1) Q = 1 kW

T = 300 k

Stransfer = Q/T = 1/ 300 = 0.0033 kW/K

2 ) Sgen = Stransfer = 0.00333 kW/K

3) Sgen = Q/350 = 1/350 = 0.002857 kW/K

4) 0.00333-0.002857 = 0.000476 kW/K

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