need help This problem addresses the power required for an automobile, which at

Question

need help

This problem addresses the power required for an automobile, which at highway speed is primarily needed to overcome air drag (this analysis neglects rolling resistance and internal engine friction).
The force of drag from air on a moving vehicle is given by Fd = 1/2 dair V2 Af Cd where dairis air density (kg/m3), V is vehicle velocity (m/s), Af is vehicle frontal area (square meters) and is Cd drag coefficient (dimensionless). Suppose an automobile with frontal area 2 m2 and with drag coefficient 0.28 is traveling at 100 km/hr and the vehicle fuel usage rate to maintain this speed is 13 km on one liter of gasoline. Gasoline has specific gravity of 0.74 and when burned completely it produces 9000 kJ/kg. Find (a) the power required to overcome air drag at this speed, and (b) the thermal efficiency of the automobile engine at this fuel-usage rate. (c) If the engine operates on a cycle with heat rejected at 20 C, what is the minimum possible combustion temperature in the engine?

Explanation / Answer

100 km/hr = 27.78 m/s

1 litre of gasoline = 0.74 kg

Fuel consumption = 13 / 0.74 km/kg = 17.568 km/kg

Energy consumption = 9000 / 17.568 = 512.308 kJ/km

a)

Air Drag force = 1/2*1.2*27.78^2*2*0.28 = 259.3 N

Power = F*v = 259.3*27.78 = 7203.4 W = 7.2034 kW

b)

Time required to cover 1 km at 27.78 m/s is 1000 / 27.78 s = 36 s

Energy consumed in 36 s = 7.2034*36 = 259.3 kJ

Efficiency = 259.3 / 512.308 = 0.5061 or 50.6 %

c)

Carnot efficiency = 1 - T_low / T_high

0.5061 = 1 - (20 + 273) / T_high

T_high = 593 K = 320 deg C

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