An automobile engine consumes fuel at a rate of 22 L/h and delivers 55 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine the efficiency of this engine.

Given Information:  

Output Power = P = 55 kW

Fuel Consumption Rate = ν = 22 L/h

Fuel Heating Value q = 44,000 kJ/kg

Fuel Density = ρ = 0.8 g/cm³

Required Information:  

Efficiency of the engine = η = ?

Efficiency of the engine = 25.56%

Explanation:

The efficiency of the engine is given by

η = P/Q

Where P is the output power and Q is the input heat supply

The heat supply is given by

Q = ρνq

Where ν is fuel consumption rate and q is the heating value of the fuel and ρ is density

First convert density from g/cm³ to kg/L

0.8*1000L/1000kg = 0.8 kg/L

Q = 0.8*22*44,000

Q = 7.74x10⁵ kJ/h

Convert kJ/h to kW     (kW and kJ/s are equivalent units)

Q = 7.74x10⁵/3600

Q = 215.11 kW

Finally, now we can find the efficiency

η = P/Q

η = 55/215.11

η = 0.2556

η = 25.56%

Therefore, the efficiency of this engine is 25.56%

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