If you purchase a plugin hybrid vehicle that costs 5000 more

If you purchase a plug-in hybrid vehicle that costs $5000 more than the same car with only a gasoline engine, determine if this purchase was economical because of the money you would save on fuel. Assume that you travel 15,000 miles per year, 5000 miles on gasoline alone, and 10,000 on plug-in electricity. The electricity costs you 7 cents per kWh, and the gasoline $2.50 per gallon (about 125.000 Btu per gallon - 131 MJ/gallon). The car requires 1000 Btu to the drive wheels to travel each mile. The battery motor combination has 80% efficiency, and the gasoline engine has 25% efficiency for the hybrid vehicle, but only averages 16% efficiency for the all-gasoline car, which obviously travels all 15,000 miles per year on the gasoline engine. The gasoline taxes collected to maintain our roads would suffer. What if all 190 million cars and pickups (including SUVs) were all plug-in hybrids, operating as designated in Problem 1, how much less gasoline would be used per year in the USA - quote use (in gallons) without hybrids, and then use if all were hybrids). At 50 cents tax per gallon of gasoline (and diesel) how much would the lost revenue be for road maintenance over a year\'s time (190 million vehicles). (Assume that the federal plus state gasoline tax throughout the nation averages what it is in Idaho, 50 cents per gallon.) The electricity needed for the plug-ins. Assume that all of the charging would be done during the evening and nighttime hours, times of low electric energy use, and that available off-peak power could be used. How much would we need to increase the installed electrical generating capacity in the USA? (Note, the installed electric capacity is about 1 million MW, and these many plants produce about 4E12 kWh per year.)

Solution

Let the cost of the gasoline engined car is $X.

Cost of hybrid car should be $X + $5000.

Assuming you travel on gasoline 5000miles and electricity 10000 miles.

1 unit of electric power = $0.07; One gallon gasoline = $2.50

Car requires 1000Btu/mile. Gasoline engine has 25% efficiency.(On hybrid vehicle.)

Gasoline car alone has, 16% efficiency.

So, to travel 1 mile Gasoline required for gasoline car is, Output/input = 0.16; Output = 1000 Btu

Input = 1000/0.16 = 6250 Btu is input energy. So, Cost of 6250Btu = 6250/125000 = 0.05 Gallons.

5 Gallons cost 2.50*0.05 = $0.125/miles. So, 15000 miles costs = 15000x0.125 = $1875 (Running on gasonline alone)

Case2) Now consider the hybrid car running for 5000 miles on gasonline.

Efficiency = 25% 1000/0.25 = 4000Btu. Cost of 4000Btu = 4000/125000 = $.032/Mile

Cost for 5000 miles = 5000*0.032 = $160

Now, for 10000miles on electricity, Efficiency = 80%,

We know, 1MJ = 3.6Kwh; 1000Btu = 0.293071Kwh

1000/0.85 = 1176.47 Btu => 0.3447893219Kwh/mile.

For 10000miles = 3447.89kwh.

1kwh =$0.07 = > 3447.89 * 0.07 =$241.35

Therefore total cost for 15000 miles on hybrid is 241.35+160 =$401.3

Gasoline alone is $1875 Which is much higher