On average in the U.S., carson light trucks, vans and SLPV’s are driven about 15

Question

On average in the U.S., carson light trucks, vans and SLPV’s are driven about 15,000 exiles per year. The average fuel economy is about 20 mpg (miles per gallon). These vehicles are mainly powered by gasoline, spark-ignition engines. The chemical energy content of gasoline is 44 MJ/kg of fuel. This Reheating value” or chemical energy is the amount of energy released when the fuel is fully burned with air in an engine or burner. It is an appropriate measure of the fuel’s ‘usable energy content.” Gasoline has a specific gravity of 0.8, slightly below that of water.

(a) Fuel economy is not the best indicator of fuel consumed. Fuel consumption, the reciprocal of fuel economy, is a more direct measure of fuel consumed. Convert 20 mpg to 11100 ken (Biters per 100 kilometers), the International 5iystem units of iuel consumption. Note that the long-term goal for cars in Europe is 3.0 l/100kxn!

(b) Calculate in kW (kilowatts) the average energy consumption corresponding to the annual mileage and average fuel economy.

(c) You are refilling the tank of your car at the service station. Estimate the chemical energy transfer rate through the refueling nozzle you hold in your hand while refueling. You will need to estimate the gasoline flow rate next time you are in the gas station. The answer is large, and illustrates why recharging electric vehicles takes a long time – several hours.

Please solve (a), (b), & (c) with explanation of detail.

Explanation / Answer

(a)

20 mpg = 20 miles / gallon
1 mile = 1.60934 km ;
1 gallon=3.78541178 liters
so 20 miles / gallon = ( 20 * 1.60934 ) / 3.78541178 km / liters ;
= 8.50285 km / liters
inversing it 1/ 8.50285 liters / km = 0. 1176075 liters / km
so for 100 km it will be
100 * 0.1176075 liters / 100 km
= 11.760758 liters / 100 km

(b) 20 miles / gallon ;
= 8.50285 e 3 m / liters
[since 1 m^3 = 1000 litres ; ]
= 8.50285 e 6 m / m^3

[ density of gasoline = 0.8 g / cm^3 = 800 kg / m^3]
[1 m^3 = 800 kg; = 800 * 44 MJ = 35200 MJ ]
= 8.50285 e 6 m / 35200 MJ
15000 miles / year = 15000 * 1.6 km /( 365 * 24 * 60 * 60 ) s = 7.6 e-4 km /s = 7.6 e -1 m/s
energy consumption = (1/ 7.6 e -1 ) * ( 8.50285 e 6 ) / 35200 e 6 J
= 3.17e-4 s / J
or taking its inverse = 1 / 3.17 e-4 W = 3150 W = 3.150 KW

(c)On average it will take approximately 4 hours to replenish the fuel consumed in 50 miles of driving (a normal daily commute) based on a vehicle consumption rate of 30 mpg
50 miles consumes 50 /30 gallon = 5/3 gallon. =( 5/3) * 800 kg = 5/3 * 800 * 44 e6 J
= 5.86 e 10 J
rate of filling = 5.86 e 10 J / ( 4* 60 * 60 ) = 3621399.17 J /s = 3.62 MJ / s
rate of energy filling = 3.62 MJ / s

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