Question

What if we could get our energy from drinking gasoline? \(^{82}\) Referring to Table \(8.2\), how many grams of gasoline \(^{83}\) would we have to drink daily to satisfy the typical 2,000 kcal/day diet? How much volume does this represent if gasoline is \(0.75 \mathrm{~g} / \mathrm{mL}\) ? Relate this to a familiar container for holding liquids. 8

Short answer

Answer: You would have to drink about 0.243 mL, or 1/20 of a teaspoon, of gasoline daily to satisfy a 2,000 kcal/day diet.

Step-by-step solution

Convert kcal to Joules

First, we need to convert the 2,000 kcal/day diet into Joules. We know that 1 kcal equals 4,184 J. Therefore, multiplying the given kcal by the conversion factor, we get: \( 2000 \; \mathrm{kcal/day} \times \dfrac{4184 \; \mathrm{J}}{1 \; \mathrm{kcal}} = 8,368,000 \; \mathrm{J/day} \)

Calculate the mass of gasoline

Next, we need to find out how many grams of gasoline are required to provide the energy needed. We are given that the energy content of gasoline is \(4.6\times10^7 \mathrm{J/g}\). Therefore, the mass of gasoline required can be calculated by dividing the energy needed by the energy content of gasoline: \( m_g = \dfrac{8,368,000 \mathrm{J}}{4.6\times10^7 \mathrm{J/g}} = 0.182 \; \mathrm{g} \)

Calculate the volume of gasoline

Now that we have the mass of gasoline required, we can calculate the volume it will occupy using the given density of gasoline. We are given that gasoline has a density of 0.75 g/mL. Therefore, dividing the mass of gasoline by the density, we get the volume required in mL: \( V_g = \dfrac{0.182 \; \mathrm{g}}{0.75\mathrm{g/mL}} = 0.243 \; \mathrm{mL} \)

Relate the volume to a familiar container

The volume we obtained is 0.243 mL, which is equal to around 0.05 teaspoons. Therefore, we would have to drink a very small amount of gasoline – just 1/20 of a teaspoon daily – to satisfy a 2,000 kcal/day diet.

Key concepts

Caloric Needs

Our bodies require energy to function, which we typically measure in calories. The average adult needs around 2,000 kilocalories (kcal) per day to maintain a healthy energy balance. This energy is used for various body functions such as digestion, physical activity, and maintaining body temperature.

Understanding caloric needs is crucial for planning diets and maintaining a healthy lifestyle. It's important to know that a kilocalorie (kcal), often just called a "calorie" in dietary terms, is a different unit from a calorie used in physics, which is smaller.

• 1 kcal = 4,184 Joules
• 2,000 kcal/day = 8,368,000 Joules/day

This means in terms of energy conversion, our daily energy needs are quite substantial, which helps set the stage for understanding the role of potential energy sources.

Gasoline Energy Content

Gasoline is primarily known as a fuel for engines, but it also contains a significant amount of energy. This makes it interesting in theoretical exercises that evaluate its potential as a human energy source.

Gasoline's energy content is approximately 46,000,000 Joules per gram. To put it into perspective, despite being highly energy-rich, it is not a suitable food because it is toxic to humans and not metabolizable. However, it is interesting to note how little gasoline, amounting to around 0.182 grams, can meet our entire daily energy need of 2,000 kcal (8,368,000 J).

• 1 gram of gasoline = 4.6 million Joules
• 0.182 grams required to meet daily 2,000 kcal requirement

The high energy density of gasoline makes it an efficient fuel for machines rather than humans.

Unit Conversion

Unit conversion is a fundamental concept in science and everyday life. It allows us to transform one set of units to another for easier interpretation and comparison.

In the context of the exercise, converting nutritional calories to joules and vice versa is essential. Knowing these conversions helps us calculate how much gasoline we would need to "consume" to meet caloric needs.

• 1 kcal = 4,184 Joules

Besides this, converting between mass and volume is necessary to understand how much space a given amount of gasoline would occupy. This is done by applying the known density formula, allowing you to see how gasoline's mass is converted to volume in milliliters.

• Density: 0.75 g/mL
• Mass to Volume conversion: 0.182 g = 0.243 mL

Mastering unit conversions makes it easier to interpret various scientific and even everyday situations accurately.

Density Calculation

Density is a measure of how much mass is contained in a given volume. It plays a crucial role when you need to convert between mass and volume, such as determining how much space an amount of gasoline will occupy.

The density of gasoline is given as 0.75 grams per milliliter (g/mL), which helps calculate its volume from a known mass. This is done using the formula: \[ V_g = \frac{m_g}{\text{Density}} \] where \( V_g \) is the volume, and \( m_g \) is the mass.

For instance, with a mass of 0.182 grams:

• Volume = 0.182 g / 0.75 g/mL = 0.243 mL

This means the volume 0.243 mL is relatively minute, equal to about 0.05 teaspoons. Such calculations help in visualizing and comparing different quantities of matter efficiently.