A particular car engine operates between temperatures of 500°C (inside the cylin

Question

A particular car engine operates between temperatures of 500°C (inside the cylinders of the engine) and 20°C (the temperature of the surroundings).

(a) Given these two temperatures, what is the maximum possible efficiency the car can have?

(b) 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 for the first part is approximately 62.1%, but I have no idea how to do the second one! PLEASE HELP :(

Explanation / Answer

a)
TL = 20 oC = (20+273) K = 293 K
TH = 500 oC = (500+273) K = 773 K
maximum possible effeciency = 1- (TL/TH)
= 1- (293/773)
= 0.62
Answer: 0.62 or 62 %

b)
vf = 100 km/hr = 100000/3600 m/s =27.78 m/s
energy required = increase in kinetic energy
= 0.5*m*(vf^2 - vi^2)
= 0.5*1500*(27.78^2 - 0)
=578703.7 J

let heat obtained be E
62% of E = energy required
0.62*E = 578703.7 J
E= 9.334*10^5 J
Answer: 9.334*10^5 J

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