Question

Question:A 5.00-grain aspirin tablet has a mass of 320 mg. For how many kilometers would the energy equivalent of this mass power an automobile? Assume 12.75 km/L and a heat of combustion of $\mathbf{3}\mathbf{.}\mathbf{65}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathit{J}\mathbf{/}\mathit{L}$ for the gasoline used in the automobile.

Short answer

Answer

The distance for energy equivalent of the aspirin tablet is$1.01\times {10}^7\text{km}$

Step-by-step solution

Identification of given data

The average of the automobile is $x=12.75\text{km}/\text{L}$

The heat of combustion of gasoline is $H=3.65\times {10}^7\text{J}/\text{L}$

The mass of the aspirin tablet is $m=320\text{mg}$

The volume of the gasoline is found by dividing the rest energy of one tablet by heat of combustion then multiply this volume with average of the automobile to find the distance travelled by automobile.

Determination of volume of the gasoline

The rest energy of aspirin tablet is given as:

$E_0=m{c}^2$

Substitute all the values in equation.

$$\begin{gathered} E_0=\left(320\text{mg}\right)\left(\frac{1\text{kg}}{{10}^6\text{mg}}\right){\left(3\times {10}^8\text{m}/\text{s}\right)}^2 \\ {E}_0=2.88\times {10}^{13}\text{J} \end{gathered}$$

The volume of the gasoline is given as:

$V=\frac{E_0}{H}$

Substitute all the values in equation.

$$\begin{gathered} V=\frac{2.88\times {10}^{13}\text{J}}{3.65\times {10}^7\text{J}/\text{L}} \\ V=7.89\times {10}^5\text{L} \end{gathered}$$

Determination of distance for energy equivalent of the aspirin tablet

The distance for the energy equivalent is given as:

$d=x·V$

Substitute all values in above equation.

$$\begin{gathered} d=\left(12.75\text{km}/\text{L}\right)\left(7.89\times {10}^5\text{L}\right) \\ d=1.01\times {10}^7\text{km} \end{gathered}$$

Therefore, the distance for energy equivalent of the aspirin tablet is $1.01\times {10}^7\text{km}$.