Q$3)$ Consider the potential carbon emissions from a gasoline$-$powered car compared with the carbon emissions to make the electricity for an electric car.

$($a$)$ Suppose the conventional car gets $40$ miles per gallon $($mpg$).$ What are the carbon emissions $($gC$/$mi$)$ assuming that gasoline contains $5\mathrm{.}22$ pounds of carbon per gallon?

$($b$)$ An efficient combined$-$cycle, natural$-$gas$-$fired power plant needs about $8,000$ kJ of heat to generate $1kWh$ of electricity. At $13\mathrm{.}8g\frac{C}{M}J$ for natural gas, what would be the carbon emissions $(g\frac{C}{m}$i for an electric vehicle that gets $5$mile$\frac{s}{k}Wh?$

$($c$)$ Suppose an older, $30$ percent$-$efficient coal$-$fired power plant generates the electricity that powers that electric car. At a carbon intensity of $24g\frac{C}{M}J$ for coal, what would the carbon emissions be $(g\frac{C}{m}$i for that $5m\frac{i}{k}Wh$ electric car? $($Hint: Assume the coal$-$fired power plant has $1kW$ input energy$)$