Please show all work Note that not all information is given

Please show all work. Note that not all information is given ON PURPOSE, and that the idea is to use estimates and physics reasoning skills.

1) Assume that a combustion-engine car driving at 70 mph uses energy at a rate of about 80 kW. Calculate the fuel efficiency of such a car. Express your answer in miles per gallon.

2) Estimate the energy stored in the battery of an electric car that has a 210 mile range. Express your answer in kWh. Note that electric motors can be 95% efficient.

3) Is it possible that someone will invent a 4-seater car that drives down highways at 70 mph and uses energy at a rate of 2 kW?

Solution

(1) V = 70 mph and energy rate at this speed E₇₀ = 80kW = 80000 J/s, density of petrol (d) = 0.75 kg/L and calorific value of petrol = 48000 kJ/kg

Distance travelled by the car in 1 hr = 70 miles and

total energy expended TE = E₇₀ x 3600 = 80000 x 3600 = 288000000 J

Amount of petrol used for TE = 288000000/48000000 = 6 kg i.e. Amount in litres = 6/0.75 = 8 litres = 2.11 gallons

So Fuel efficiency = 70 / 2.11 = 33.2 miles/gallon (ANSWER)

(2) Distance range d = 210 miles = 337962.2m (Assume that distance will be travelled in 2.5 hr)

Mechanical work (Mw) that can be done by the electric motor assuming car mass of 1000kg = 1000 x 9.81 x d =

= 1000 x 9.81 x 337962.2 = 3315409182 J

Efficiency of electric motor E = 95%, So Energy stored in battery/Energy input Be = Mw / E = 3315409182 / 0.95

So Be = 3489904402.1 J = 3489904.4 kJ i.e. in kWh it will be Be/2.5 = 3489904.4/2.5 = 1395961.8 kWh

So Energy stored in battery = 1395961.8 kWh (ANSWER)

(3) Speed of 4 seater car S = 70 mph = 31.3 m/s, Energy input Ein = 2kW = 2000W.

Assuming typical vehicle efficiency of 40%, amount of mechanical power available (Mw) = 0.40 x Ein

i.e. Mw = 0.40 x 2000 = 800 W Now let \'m\' be the mass of the 4-seater car

By formula Mw = m x 9.81 x S i.e. 800 = m x 9.81 x 31.3 i.e. m = 2.6 kg

This mass / weight m = 2.6 kg is not possible, hence the 4-seater car is not possible. (ANSWER)