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\(\bullet\) \(\bullet\) U.S. power use. The total consumption of electrical energy in the United States is about \(1.0 \times 10^{19}\) joules per year. (a) Express this rate in watts and kilowatts. (b) If the U.S. popu- lation is about 310 million people, what is the average rate of electrical energy consumption per person?

Short Answer

Expert verified
(a) Approximately \(3.17 \times 10^{11}\) W or \(3.17 \times 10^{8}\) kW. (b) Average per person is \(1023\) W or \(1.023\) kW.

Step by step solution

01

Convert Joules per Year to Watts

Power is the rate at which energy is consumed, calculated as energy per unit of time. Use the conversion factor of 1 year to seconds. There are \(365 \times 24 \times 3600 = 31,536,000\) seconds in a year. Given the total energy consumption is \(1.0 \times 10^{19}\) joules per year, the power in watts (W) is calculated as:\[ \text{Power (W)} = \frac{1.0 \times 10^{19} \, \text{joules/year}}{31,536,000 \, \text{seconds/year}} \approx 3.17 \times 10^{11} \, \text{W} \]
02

Convert Watts to Kilowatts

To find the power in kilowatts (kW), convert watts to kilowatts by recognizing that 1 kilowatt is equal to 1000 watts:\[ \text{Power (kW)} = \frac{3.17 \times 10^{11} \, \text{W}}{1000} \approx 3.17 \times 10^{8} \, \text{kW} \]
03

Calculate Average Consumption per Person

To find the average electrical consumption per person, divide the total power consumption by the population. Given 310 million people, calculate the average power per person in both watts and kilowatts:\[ \text{Average Power per Person (W)} = \frac{3.17 \times 10^{11} \, \text{W}}{310 \times 10^{6}} \approx 1023 \text{ W/person} \]Convert this to kilowatts:\[ \text{Average Power per Person (kW)} = \frac{1023 \, \text{W}}{1000} \approx 1.023 \, \text{kW/person} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Power Consumption
Power consumption is an essential factor when considering how much energy is used over time. Think of it as the speedometer of energy usage—it tells us how fast we're consuming energy resources.

When we say the power consumption is high, it means a lot of energy is being used in a short amount of time. In the case of the United States, an enormous amount of electrical energy—approximately \(1.0 \times 10^{19}\) joules per year—is consumed.

So how do we determine the power from this energy usage? We convert the energy from joules (a unit of energy) to watts (a unit of power). Power is defined as energy per time, so we need to know how much energy is used for every second of the year. By calculating the number of seconds in a year to be 31,536,000 and dividing the total energy by this number, we convert the yearly energy to watts. This could be visualized like slicing a big pie into many smaller daily or hourly portions!
Joules to Watts Conversion
Converting joules to watts is a crucial step in measuring power usage over time. Watts represents the rate of energy consumption, which is derived from energy units like joules used over a particular time period, such as a second.

To effectively manage and understand energy efficiency, such conversion is necessary. The conversion process involves dividing the total energy in joules by the total time in seconds that the energy is consumed.

For instance, the power consumption in the U.S. is calculated by dividing \(1.0 \times 10^{19}\) joules by the total seconds in a year, which is 31,536,000. This calculation helps us understand how electrical energy translates into continuous power usage in watts.

This method provides a universal standard (the watt) that makes it easier to compare energy consumptions across various platforms and regions, offering a common language to discuss electrical efficiency and needs.
Average Power per Person
Calculating the average power consumption per person shows us the amount of energy each individual would use if the total energy were distributed equally among the population. This step offers a fascinating insight into per capita energy use, a significant indicator of lifestyle and technological impact on energy needs.

For the U.S., with a population of 310 million people, we first find the total power consumption in watts from our previous calculation. This result, \(3.17 \times 10^{11}\) watts, is then divided by 310 million people.

The result is about 1023 watts per person, showing us that each person, on average, uses this much power every second. Converting this to kilowatts (by dividing by 1,000) gives approximately 1.023 kilowatts per person.

This number is significant as it indicates not just energy consumption but also various aspects of modern living, showing the technological demands each person's lifestyle places on power resources.

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Most popular questions from this chapter

\(\bullet\) (a) How many joules of energy does a 100 watt lightbulb use every hour? (b) How fast would a 70 kg person have to run to have that amount of kinetic energy? Is it possible for a per- son to run that fast? (c) How high a tree would a 70 kg person have to climb to increase his gravitational potential energy rela- tive to the ground by that amount? Are there any trees that tall?

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