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Question

A motor cycle engine delivers a power of 10 kW by consuming petrol at the rate of 2.4 kg/hr. Find the rate of heat rejection by the exhaust, if the calorific value of petrol is 35.5 MJ/kg.
(Neglect the other losses)

A
13.7 kW
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B
23.7 kW
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C
33.7 kW
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D
13.7 W
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Solution

The correct option is A 13.7 kW
Let Q1 be the consumption of heat by engine, and Q2 be the rejection of heat by engine, W be the work done by engine
The rate at which heat is consumed by engine will be,
Q1dt=2.4×35.5×106 J/hr
Q1dt=85.2×1063600 J/sec=23.7 kW
Rate of rejection of heat is given by Q2dt,
Applying energy conservation,
Q1=Q2+W ...(i)
Q2=Q1W
Differentiating both sides w.r.t time,
dQ2dt=dQ1dtdWdt ...(ii)
where dWdt=10 kW, is the rate of workdone or the power delivered by engine.
dQ2dt=23.7 kW10 kW
dQ2dt=13.7 kW
Hence, the rate of heat rejection by exhaust is 13.7 kW

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