Question

If an average American is responsible for consuming a barrel \(^{80}\) of oil every 18 days, what power does this correspond to, in Watts?

Short answer

Based on the given information, calculate the power consumption of an average American in watts, if they consume 80 barrels of oil every 18 days, and 1 barrel is equivalent to 6.1 × 10^9 Joules of energy.

Step-by-step solution

Write down the given information and the conversion factor

An average American consumes 80 barrels of oil every 18 days, and we know that 1 barrel of oil is equivalent to 6.1 × 10^9 Joules of energy.

Calculate the total energy consumed in 18 days

To find the total energy consumed, we simply multiply the number of barrels consumed with the energy per barrel: Total_energy = NumberOfBarrels × EnergyPerBarrel Total_energy = 80 × 6.1 × 10^9 J

Calculate the energy consumed per second

Next, we need to find out how much energy is being consumed per second. To do this, we will divide the total energy consumed by the number of seconds in 18 days: Seconds_in_18_days = 18 × 24 × 60 × 60 Energy_per_second = Total_energy / Seconds_in_18_days Energy_per_second = (80 × 6.1 × 10^9 J) / (18 × 24 × 60 × 60)

Convert the energy per second to Watts

Since power (in watts) is energy consumed per unit time, and we have already calculated the energy consumed per second, this value is equivalent to the power consumption in Watts: Power = Energy_per_second Power = (80 × 6.1 × 10^9 J) / (18 × 24 × 60 × 60)

Calculate the final answer

Now, we can compute the power consumption by plugging in the numbers and perform the calculations: Power = (80 × 6.1 × 10^9 J) / (18 × 24 × 60 × 60) ≈ 31067.13 W So, the power consumption of an average American corresponding to the given oil consumption is approximately 31,067.13 Watts.

Key concepts

Power Calculation

When we talk about power in physics, it generally refers to the rate at which energy is used or consumed. Power is essentially how fast work is done. It is calculated using the formula:

• Power = Energy ÷ Time

This means that if you know how much energy is consumed and how long it takes, you can find the power. In the earlier exercise, we calculated the power consumption by dividing the total energy consumed in 18 days by the number of seconds in those days. The goal was to determine how many Joules are used per second. Remember, knowing the rate of energy consumption is crucial for understanding the design and efficiency of power systems in everyday life.

Joules to Watts Conversion

When you come across energy and power, it's vital to understand the relationship between Joules and Watts. Energy is measured in Joules, and power is measured in Watts. One Watt is equivalent to one Joule per second. So you can think of Watts as a measure that tells you how quickly energy is being used.
In the exercise, we use this conversion to find out how much energy in Joules turns into power in Watts. By using the formula:

• Watts = Joules ÷ Seconds

we see that when we have energy in Joules consumed over a certain time in seconds, converting it to Watts gives us a handy way to understand the power used. This conversion is consistent in physics and helps us quantify energy use across various applications.

Energy Consumption Analysis

Understanding energy consumption involves analyzing how much energy is used over a period, which helps in determining efficiency and planning usage. In our exercise, we look at energy consumption in terms of barrels of oil, converting it to Joules.
Here's how you can analyze energy consumption:

• First, identify the total energy consumed, which is the product of the number of units consumed (such as barrels of oil) and the energy per unit.
• Second, break down this energy into smaller time segments, like per second, to understand the consumption rate.

This type of analysis is internal to energy planning, as it allows us to gauge the impact of energy on resources and costs, and it contributes to better energy management strategies.

Mathematics in Physics

Mathematics is the language of physics and plays a vital role in solving physical problems. It allows us to calculate, model, and predict physical phenomena. In this case, math helps convert quantities and interpret measures like energy and time.
In physics, mathematical formulas help bridge concepts with real-world phenomena, such as calculating power or energy. Working through the step-by-step math in the exercise involves:

• Multiplying to find total energy consumption (Joules).
• Dividing to convert energy (Joules) to power (Watts) per second.

This exercise is a great example of how mathematics provides clarity in physical concepts, by performing calculations that transform conceptual ideas into tangible numbers. Mastery in both mathematics and physics allows you to articulate and solve complex problems more effectively.