Energy and Power

The time has come, the walrus said, to talk of many things. And I say it’s time to address a few recent comments. Let me begin with Akshay’s comment:

Quoth he:

You are right that energy is not an immediate limit to growth. While total energy usage today is about 20 TW (20E12 Watts), solar energy received by Earth at any given time is about: pi * R^2 * Solar_constant = 3.14 * 6.378E6^2 * 1.361E3 = 173843 TW. So, yes there is enormous room for growth in energy usage.

Them are impressively large numbers. It makes my brain numb. But let me being.

It is not debatable that energy powers the world. Interestingly, people usually confuse the terms energy and power, and use them interchangeably. I confess it is easy to do so, as Akshay did in the quoted bit above. He wrote watts but the proper SI unit is joules. Watts is a measure of power; joules is a measure of energy.

I need a quick tutorial on a few basic physics terms: mass, distance, force, work, energy and power. So here goes.

Mass is measured in kilograms. Distance is measured in meters. Force is measured in newtons (N). Force is mass times acceleration. One newton of force accelerates one kilogram mass by one meter per second squared. Force times distance is work. Work is defined in joules (J). So one joule is the work done (energy consumed) by a force of one newton over one meter. Work and energy are equivalent because you need energy to do work. Therefore, work or energy is measured in joules.

    • Kilogram – mass
    • Meter – distance
    • Force – newton. 1 newton accelerates one kilogram mass by 1 m/s2.
    • Work (energy) – joules. Work is force times distance. 1 joule is the energy equivalent of 1 newton force applied over 1 meter.
    • Power – watts. Energy per second. Therefore joules per second. 1 watt is 1 joule per second. A 100 watt (power) lamp consumes (dissipates as heat and light) 100 joules of energy per second.

Globally, the total energy used by the ~8 billion people over a year now is a little over 180,000 terajoules terawatt-hours. (See Our World in Data.) That’s a lot of energy.

To translate that into power that humans use (though why would one want to do that is not clear), divide the energy used by the number of seconds in a year and you will get the average power consumption in watts, or whatever units strike your fancy.

My guess is that it will be a lot more than 100 watts. How much more? I leave that as an exercise for the interested reader. You do the arithmetic. Or just ask one of them AIs on the web. Remember that those who refuse to do arithmetic are doomed to speak nonsense, as dear John McCarthy used to say.

That was exhausting. So I have to continue in the next bit.

Here’s the next bit: Limits to Growth

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Author: Atanu Dey

Economist.

3 thoughts on “Energy and Power”

  1. It is common to use energy and power interchangeably, with the unit (Joules/cal/Cal/Btu/Quads vs. Watts/Horsepower) making clear what is meant. But, yes I agree it is better to be more precise to avoid mistakes or miscommunication. By the way, you made a mistake when quoting the yearly energy use from ourworldindata: it is 180,000 TWh (Tera Watt Hours [1]) per year and not 180,000 TJ (Tera Joules). 180,000 TWh of energy per year works to an average power consumption of 20.548 TW (Tera Joules/sec), which agrees with what I quoted earlier: ~20TW.

    Anyway, the reason I quoted power usage (Watts), instead of yearly energy usage (Joules) was to make it easy to compare to the continuous solar irradiance power received by Earth: pi * R^2 * Solar_constant = 3.14 * 6.378E6^2 * 1.361E3 = 173,843 TW, which is about 4 orders of magnitude greater!

    Also, the total power usage per capita is worth comparing with the bodily per capita power consumption (obtained from food):

    20 TW / 8 billion = 2568.49 Watts per capita

    Assuming a 2000 Calorie/day diet:

    2000 * 1E3 * 4.184 / (3600*24) = ~100 Watts [2]

    The one order of magnitude difference should make clear William Catton’s observation [3] that we are no longer in the age of Homo sapiens, but in the age of Homo colossus. But, the bottom line is that despite already consuming colossal amounts of energy, this is still peanuts compared to the cosmic energy from solar fusion received on Earth. In other words, energy is not yet a limit to growth. BUT, even at a measly 5% year-on-year energy consumption growth, in a mere 186 years, this limit will be breached!

    [1] Most likely used because kWh (kilo Watt hour) is a common energy unit for measuring residential electric energy consumed.

    [2] Somewhat confusingly 1 Calorie = 1000 calorie, and 1 calorie = 4.184 Joules, which is the famous mechanical equivalent of heat measured by James Prescott Joule.

    [3] https://en.wikipedia.org/wiki/William_R._Catton_Jr.#The_legacy_of_Catton's_1980_book,_Overshoot

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    1. First of all, thanks for catching the mistake I made in reporting “terajoules” instead of “terawatthours.” I plead a momentary lapse of attention, probably induced by hunger. I am in charge of food and I frequently forget that fact.

      I will address your other points in a follow up post.

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