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A 1800 kg hybrid vehicle operates on ethanol and is equipped with a multipurpose motorgenerator-flywheel. When the vehicle slows or stops, 50% of the kinetic energy is recovered as electrical energy in the battery. When the IC engine is used to recharge the battery, there is a 25% efficiency of converting chemical energy in the fuel to electrical energy stored in the battery. The vehicle slows from 70 miles per hour to 20 miles per hour. Calculate:

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A 1800 kg hybrid vehicle operates on ethanol and is equipped with a multipurpose motorgenerator-flywheel. When the vehicle slows or stops, 50% of the kinetic energy is recovered as electrical energy in the battery. When the IC engine is used to recharge the battery, there is a 25% efficiency of converting chemical energy in the fuel to electrical energy stored in the battery. The vehicle slows from 70 miles per hour to 20 miles per hour. Calculate: (A) Electrical energy recovered in the battery in [kJ] (B) Mass of fuel needed to store same amount of energy in the battery in [kg]

Answer:

a) Electrical energy recovered in the battery is 404.6895 kJ

b) Mass of fuel needed to store same amount of energy in the battery is 0.0606 kg

Explanation:

Given that;

Initial speed of the vehicle V = 70 miles per hour = 31.293 m/s

Final speed of the vehicle u = 20 miles per hour = 8.941 m/s

mass of vehicle m = 1800 kg

Noe, change in kinetic energy of the vehicle will be;

[tex]E_{kinetic}[/tex] = [tex]\frac{1}{2}[/tex]m( v² - u² )

we substitute

=  [tex]\frac{1}{2}[/tex] × 1800( (31.293)² - (8.941)² )

= 900( 979.2518 - 79.9414)

= 900 × 899.3104

=  809379.36 J

[tex]E_{kinetic}[/tex] = 809.379 kJ

now, Electrical energy recovered in the battery when the vehicle slows will be;

[tex]E_{battery}[/tex] = 50% × [tex]E_{kinetic}[/tex]

[tex]E_{battery}[/tex] = 50/100 × 809.379 kJ

[tex]E_{battery}[/tex] =  404.6895 kJ

Therefore, Electrical energy recovered in the battery is 404.6895 kJ

b)

For this electrical energy to be obtained from fuel, the chemical energy required will be;

[tex]E_{chemical}[/tex] =  [tex]E_{battery}[/tex] / 25%

[tex]E_{chemical}[/tex] =  404.6895 kJ / 0.25

[tex]E_{chemical}[/tex]  = 1618.758 kJ  

Heat energy released per mass of ethanol combustion

(Lower heating value of ethanol) is 26.7kJ/g

Now, the mass of fuel needed to generate  1618.758 kJ will be;

[tex]m_{fuel}[/tex] = 1618.758 kJ / 26.7kJ/g

[tex]m_{fuel}[/tex] = 60.63 g

[tex]m_{fuel}[/tex] = 0.0606 kg

Therefore, Mass of fuel needed to store same amount of energy in the battery is 0.0606 kg

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