# Answer to Question #42950 in Physical Chemistry for Zeph

Question #42950

If the fuel consumption of a car, travelling at a steady 60 mph is 20 mpg what is the power produced by the petrol being burnt in the engine ? (Assume that the density of petrol is 0.84 kg/l and the heat of combustion of petrol is 47 302 kJ/kg. I need the calculations

Expert's answer

Solution:

Answer:

If the British imperial gallon is used to measure the petrol consumption, the power is equal to 150.5 kJ/s.

If the US liquid gallon is used to measure the petrol consumption, the power is equal to 125.3 kJ/s.

`Consider the car riding for 1 hour. It traveled a distance of 60 mph * 1 hour = 60 miles. The petrol`

consumption is 60 miles / 20 mpg = 3 gallons of petrol.

There are two different relations between gallon and liter:

1) The British imperial gallon: 1 gal = 4.5461 l

2) The US liquid gallon: 1 gal = 3.7854 l

The further calculation will consider both options.

The petrol consumption in liters is equal to:

(1): 3 gal * 4.5461 l/gal = 13.638 l

(2): 3 gal * 3.7854 l/gal = 11.356 l

The mass of petrol can be calculated multiplying the volume by density:

(1): 0.84 kg/l * 13.638 l = 11.456 kg

(2): 0.84 kg/l * 11.356 l = 9.539 kg

The energy evolved from the petrol combustion can be calculated as follows:

(1): 47 302 kJ/kg * 11.456 kg = 541 892 kJ

(2): 47 302 kJ/kg * 9.539 kg = 451 213 kJ

The power is the energy per unit of time. Power = Energy / Time

(1): P = 541 892 kJ / 1 hour = 541 892 kJ / 3600 s = 150.5 kJ/s

(2): P = 451 213 kJ / 1 hour = 451 213 kJ / 3600 s = 125.3 kJ/s

Answer:

If the British imperial gallon is used to measure the petrol consumption, the power is equal to 150.5 kJ/s.

If the US liquid gallon is used to measure the petrol consumption, the power is equal to 125.3 kJ/s.

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