Question

The table shows fuel efficiency for several automobiles.

(a) A mile is 5280feet and a foot is 12inches. Use Table $\mathbf{1}\mathbf{-}\mathbf{4}$to find how many miles are in 1km.

(b) The gasoline-engine Peugeot 107consumes 4.6Lof fuel per 100km. Express the fuel efficiency in miles per gallon. A U.S. liquid gallon is 3.7854L.

(c) The diesel Cabriolet is more efficient than the gasoline Cabriolet. How many metric tons CO₂ ofare produced by the diesel and gasoline Cabriolets in 15000miles of driving? A metric ton is 1000kg.

Short answer

a) $1\mathrm{km}=0.62137\mathrm{miles}$

b) The fuel efficiency is $51miles/gallon$

c)The CO₂ produced by diesel and gasoline are 5.38 metric tons and 6.42 metric tons respectively.

Step-by-step solution

Definition of fuel efficiency

Fuel efficiency is a measurement of how well an automobile converts the energy in its fuel into kinetic energy for travel.

Step 2:Finding the miles in .

(a)

$$\begin{gathered} 1mile=5280feet \\ 1foot=12inches \\ 1\mathrm{km}=1000\mathrm{m}\times \left(\frac{1\mathrm{in}}{0.0254\mathrm{m}}\right)\times \left(\frac{1\mathrm{foot}}{12\mathrm{in}}\right)\times \left(\frac{1\mathrm{mile}}{5280\mathrm{feet}}\right) \\ =0.62137\mathrm{miles} \end{gathered}$$

Step 3:Finding the fuel efficiency

(b)

$$\begin{gathered} fuelefficiency=\frac{100\mathrm{km}}{4.6\mathrm{L}}\times \left(\frac{0.62137}{1\mathrm{km}}\right)\times \left(\frac{3.7854\mathrm{L}}{1\mathrm{gallon}}\right) \\ =51miles/gallon \end{gathered}$$

Step 4:Finding the produced by diesel and gasoline.

(c)

The diesel Cabriolet produces$223{\mathrm{gCO}}_2/\mathrm{km}$

The total mass of${\mathrm{CO}}_2$produced is calculated as:

$$\begin{gathered} Thetotalmass=15000\mathrm{miles}\times \left(\frac{1\mathrm{km}}{0.62137\mathrm{miles}}\right)\times \left(\frac{223{\mathrm{gCo}}_2}{1\mathrm{km}}\right)\times \left(\frac{1\mathrm{kg}}{{10}^3\mathrm{g}}\right)\times \left(\frac{1\mathrm{metric}\mathrm{ton}}{{10}^3\mathrm{kg}}\right) \\ =5.38\mathrm{metric}\mathrm{tons} \end{gathered}$$

The gasoline Cabriolet produces $266{\mathrm{gCO}}_2/\mathrm{km}$

The total mass of CO₂ produced is calculated as:

$$\begin{gathered} Thetotalmass=15000\mathrm{miles}\times \left(\frac{1\mathrm{km}}{0.62137\mathrm{miles}}\right)\times \left(\frac{266{\mathrm{gCo}}_2}{2}\right)\times \left(\frac{1\mathrm{kg}}{{10}^3\mathrm{g}}\right)\times \left(\frac{1\mathrm{metric}\mathrm{ton}}{{10}^3\mathrm{kg}}\right) \\ =6.42\mathrm{metric}\mathrm{tons} \end{gathered}$$