Question

A particular car engine operates between temperatures of 400°C (inside the cylinders of the engine) and 20°C (the temperature of the surroundings).
Given these two temperatures, what is the maximum possible efficiency the car can have? (Note that actual car engine efficiencies are in the 20-25% range.)
_______ %

Part (b)

A particular car engine operates between temperatures of 400°C (inside the cylinders of the engine) and 20°C (the temperature of the surroundings).
If the car was somehow able to operate at its 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). Note that a number like 1.23x10^9 can be entered as 1.23e9
_______ J

Answer 1

Temperature inside the cylinders of the engine = T_h = 400 ^oC = 400 + 273 K = 673 K

Surrounding temperature = T_c = 20 ^oC = 20 + 273 K = 293 K

Maximum possible efficiency of the car =

Maximum possible efficiency of an engine is the carnot efficiency.

= 0.5646

= 56.46%

Mass of the car = m = 1500 kg

Initial speed of the car = V₁ = 0 m/s (At rest)

Final speed of the car = V₂ = 100 km/hr = 100 x (1000/3600) m/s = 27.778 m/s

Work done by the engine on the car = W

The change in kinetic energy of the car is equal to the work done by the engine.

W = mV₂²/2 - mV₁²/2

W = (1500)(27.778)²/2 - (1500)(0)²/2

W = 5.787 x 10⁵ J

Heat to supplied by the fuel to the engine to do this much amount of work = Q_h

Q_h = 1.025 x 10⁶ J

a) Maximum possible efficiency of the car engine = 56.46%

b) Heat supplied by the fuel to the engine to accelerate the car from rest to 100 km/hr = 1.025 x 10⁶ J