Question

Let's say that in the course of one year a county in Texas produces 5 million \(\mathrm{kWh}\) of electrical output from wind, and also pumps 100,000 barrels of oil from the ground containing a (thermal) energy content of about 6 GJ per barrel. What percentage of total energy production came from wind, if scaling wind in terms of thermal equivalent, as explained in Box \(7.2 ?\)

Short answer

Answer: The percentage of total energy production that came from wind energy can be found by calculating the expression: \(\dfrac{5 \times 10^6 \mathrm{kWh} \times 3,600,000 \mathrm{J/kWh}}{(5 \times 10^6 \mathrm{kWh} \times 3,600,000 \mathrm{J/kWh}) + (100,000 \text{ barrels} * 6 \times 10^9 \mathrm{J/barrel})} \times 100\%\)

Step-by-step solution

Calculate the energy produced by wind

To find the energy produced by wind, we are given that the wind energy production is \(5\) million kWh. We need to convert this to the thermal equivalent. According to Box 7.2, \(1 \mathrm{kWh}\) (of electricity) is considered equivalent to \(3,600,000 \mathrm{J}\) (of heat). So, we can calculate the thermal energy from wind as follows: Wind energy (in J) = Wind energy (in kWh) * Conversion factor Wind energy (in J) = \(5 \times 10^6 \mathrm{kWh} * 3,600,000 \mathrm{J/kWh}\)

Calculate the energy produced by oil

We are given that the county in Texas produces \(100,000\) barrels of oil, with an energy content of \(6 \mathrm{GJ}\) per barrel. Therefore, we can calculate the energy produced by oil as: Oil energy (in J) = Number of barrels * Energy per barrel Oil energy (in J) = \(100,000 \text{ barrels} * 6 \times 10^9 \mathrm{J/barrel}\)

Calculate total energy produced

To find the total energy, we need to add the energy produced by wind and oil: Total energy (in J) = Wind energy (in J) + Oil energy (in J)

Calculate the percentage of energy from wind

To find the percentage of energy from wind, we'll divide the wind energy by the total energy and multiply by 100%: Percentage from wind = \(\dfrac{\text{Wind energy (in J)}}{\text{Total energy (in J)}} \times 100\%\) Now, plug in the values from Steps 1 and 3: Percentage from wind = \(\dfrac{5 \times 10^6 \mathrm{kWh} \times 3,600,000 \mathrm{J/kWh}}{(5 \times 10^6 \mathrm{kWh} \times 3,600,000 \mathrm{J/kWh}) + (100,000 \text{ barrels} * 6 \times 10^9 \mathrm{J/barrel})} \times 100\%\) By calculating this expression, we find the percentage of total energy production that came from wind.

Key concepts

Thermal Energy

Thermal energy is a form of energy associated with the temperature of an object. This energy results from the movement of particles within a substance. When we think about things like a warm cup of coffee or the sun warming the ground, we're observing thermal energy in action. Thermal energy can be converted from one form to another, such as from chemical energy in fuel to heat during combustion, or from kinetic energy to heat during friction.
In the context of energy production, it's vital to understand how we measure and convert thermal energy.

• In the provided exercise, you encounter two energy forms: electrical output from wind energy and thermal energy from oil.
• Electricity generated from wind is typically measured in kilowatt-hours (kWh).
• In contrast, oil's energy content is given in gigajoules (GJ) per barrel. 1 kWh equates to 3,600,000 joules (J), aligning the wind-derived electrical energy to thermal units for comparison to oil.

This conversion is crucial for comparing different energy sources, as it sets a common ground for various energy forms using thermal energy as a reference. Recognizing thermal energy's role allows us to gauge how different resources contribute to overall energy production.

Electrical Output Calculation

Electrical output calculation essentially centers on determining the total energy produced in electrical form. In our scenario, we're looking at wind energy contribution, expressed initially in kilowatt-hours (kWh). To effectively compare this energy with the thermal energy from oil, we need to convert it into joules (J). When calculating the energy from wind, observe the following steps:

• First, understand that 1 kWh is equal to 3,600,000 J, a critical conversion factor.
• Using the formula, you need to multiply the given energy production (in kWh) by this factor to convert into joules.
• This converged energy allows it to be measured against other forms of energy, such as the thermal energy in oil to understand the total dynamics of energy production from wind.

In practice, this calculation reveals the underlying efficiencies and contributions of renewable resources like wind power in the broader energy mix. Understanding your electrical output in joules helps you appreciate its role compared to other energy types, including traditional fossil fuels.

Percentage Calculation

Once we have determined the thermal energy equivalency for both the wind and oil, we can now calculate the wind's contribution to the total energy production in percentage terms. This calculation gives a clearer insight into how significant wind power is as an energy source compared to oil. First, compute the total energy produced by summing up the energies from both wind and oil sources.

• It's essential because, without knowing the total, you can't figure out how large a share wind energy takes up.
• The formula to calculate the percentage is: \[\text{Percentage from wind} = \dfrac{\text{Wind energy (in J)}}{\text{Total energy (in J)}} \times 100\%\]
• Plug in the appropriate values to this formula to ascertain the specific percentage.

Understanding percentage calculations in energy contexts helps discern which sources are most impactful in a given scenario.
This kind of analysis is invaluable for energy strategists who aim to balance renewable energy sources with traditional ones.