A particular heat engine has a useful power output of 6.50 kW and an efficiency

Question

A particular heat engine has a useful power output of 6.50 kW and an efficiency of 37.5%. In each cycle, the engine expels 8.75 kJ of exhaust energy. Find the energy taken in during each cycle the time interval for each cycle If the Carnot's engine of the same efficiency operates with the cold reservoir at room's temperature (22 degree C), find the temperature of the hot reservoir of the Carnot's engine. - Power = rate at which Energy or Work are used (or P = W/t) - Prefix "kilo" means "1000 times" - Care should be taken when applying formulas to ensure that properties with the correct units are used

Explanation / Answer

Solution:

a) The engine wastes 8750J each cycle.

At 37.5% efficiency, that means 0.625Q is exhausted (wasted),

so 0.625Q = 8750J, and Q = 14000 J (total energy per cycle).

Power output = 6.50 kW = 6500 J/s
Useful energy per cycle = (0.375)(14000) = 5250 J/cycle

(b) The engine will have to cycle 6500/5250 times a second = 1.238 cycles per second, or 1/1.238 = 0.807s per cycle

c) We know that carnot efficiency = 1 - (Tc/Th)

but efficiency = 37.5% = 0.375 and Tc = 22oC = 295K

therefore

0.375 = 1 - (295/Th)

Th = 472K = 199oC

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