A particular car engine operates between temperatures of 450°C (inside the cylin

Question

A particular car engine operates between temperatures of 450°C (inside the cylinders of the engine) and 20°C (the temperature of the surroundings).

The maximum possible efficiency is 59.5%

With this maximum efficiency, determine how much heat must be obtained by burning fuel in the car's engine to accelerate a 1500 kg car from rest to a speed of 100 km/h (neglect resistive forces).

The answer is 9.73 x 10^5

Please explain

I found that 100 km/h is 27.78 m/s so the work would be the change in kinetic energy:

1/2mv^2=1/2 x 1500kg x 27.78^2 = 578,796.3 J

I don't know where to go from here...

Explanation / Answer

578,796.3 J is required heat but engine has to produce more because its efficiency is 59.5 only so let required heat production be x then

x * 59.5 /100 = 578796.3

x = 972766.890756

= 9.73 *10^5 J

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