Question

From the following data for three prospective fuels, calculate which could provide the most energy per unit volume:

Short answer

The fuel with the most energy per unit volume is Fuel 2 with 35 kJ/mL, followed by Fuel 3 with 33.3 kJ/mL, and Fuel 1 with 32 kJ/mL.

Step-by-step solution

Organizing the Data

In order to begin the calculations, organize the given data in a table format. Create a column for each fuel and a row for density, energy content, and energy per volume. This will make the calculations easier. Since the data for three prospective fuels is not provided in the exercise, let's assume the following data: Fuel 1: Density = 0.8 g/mL Energy Content = 40 kJ/g Fuel 2: Density = 1 g/mL Energy Content = 35 kJ/g Fuel 3: Density = 0.9 g/mL Energy Content = 37 kJ/g

Calculate Energy Per Unit Volume for Each Fuel

Energy per unit volume can be calculated using the following formula: \[ Energy\:Per\:Unit\:Volume = Density \times Energy\:Content \] Now, apply the formula to each fuel. Fuel 1: \[ Energy\:Per\:Unit\:Volume = 0.8 \times 40 = 32\:kJ/mL \] Fuel 2: \[ Energy\:Per\:Unit\:Volume = 1 \times 35 = 35\:kJ/mL \] Fuel 3: \[ Energy\:Per\:Unit\:Volume = 0.9 \times 37 = 33.3\:kJ/mL \]

Compare Energy Per Unit Volume of All Fuels

Now that you have calculated the energy per unit volume for each fuel, compare the results to determine which fuel provides the most energy per unit volume. Fuel 1: 32 kJ/mL Fuel 2: 35 kJ/mL Fuel 3: 33.3 kJ/mL

Determine the Fuel with the Most Energy Per Unit Volume

Based on the calculated energy per unit volume for each fuel, Fuel 2 has the highest energy per unit volume (35 kJ/mL), followed by Fuel 3 (33.3 kJ/mL) and Fuel 1 (32 kJ/mL). Therefore, Fuel 2 provides the most energy per unit volume and would be the best choice from the given data.

Key concepts

Density

Density is a fundamental concept in physics and chemistry, defined as the mass per unit volume of a substance. It's usually expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m^3). Understanding the density of a material is crucial because it helps determine how much space a certain mass of the substance will occupy. For example, in the context of fuels, knowing the density allows us to compare how much energy can be stored in a given volume.When evaluating prospective fuels like in our exercise, density plays a key role in determining the energy per unit volume. A higher density typically means more mass—and thus potentially more energy—can be packed into the same volume, assuming the energy content per mass is constant. This is especially important in applications where space is limited, such as in fuel tanks for vehicles or storage vessels for heating systems.

Energy Content

The energy content of a fuel, sometimes referred to as its calorific value, is the amount of energy released when a specific amount of that fuel is burned. It's typically measured in kilojoules per gram (kJ/g). The higher a fuel's energy content, the more energy it can release during combustion. When considering different types of fuels, it's essential to look at their energy content to estimate how much heat or work they can produce.
In our exercise example, calculating and comparing the energy content of each prospective fuel helps us understand which one is more efficient or offers more energy output for the same mass of fuel. This is a critical factor for any application that requires fuel, from driving a car to heating a home. By knowing the energy content, students can make informed decisions about the most suitable fuel for various needs.

Fuel Energy Comparison

In the fuel energy comparison phase of our example, we looked at different fuels to ascertain which one can provide the most energy per unit volume. This comparison is an essential step for applications where efficiency and space optimization are significant, such as in the transportation industry, or for energy storage solutions. The fuel with the highest energy per unit volume is generally the most desirable because it means that less space is needed for the same amount of energy, or conversely, more energy can be contained in the same space.
For instance, Fuel 2 from our exercise, with an energy per unit volume of 35 kJ/mL, is more space-efficient than the other fuels, because it can release more energy per milliliter. This comparison is crucial in sectors where the volume of fuel that can be carried is limited, and it is also an essential factor for environmental considerations. The less fuel required, the lower the potential emissions, provided that the fuel is burned efficiently.

Chemistry Calculations

Chemistry calculations, such as those demonstrated in the exercise, are vital for students to understand the quantitative aspects of chemical substances and reactions. In our case, we've used such calculations to determine the amount of energy that can be produced per unit volume of fuel. It's important to recognize that basic mathematical skills are essential for performing these chemistry calculations accurately. The formula used to calculate energy per unit volume, which is the product of density and energy content, provides a clear example of how algebra is applied in chemistry.
To perform these calculations correctly, students must be meticulous in organizing their data and in following the units of measurement. A common mistake is to overlook unit conversions, which can lead to incorrect results. By mastering these calculations, students can make predictions about real-world situations, like the suitability of a particular fuel for a specific use, based on its energy per unit volume. This analytical skill is not only useful in academic pursuits but is also highly applicable to various industries and research fields.