# Thermodynamic limits of human energy consumption as imposed by the Earth

Published 16 February 2014

It is well known that human energy consumption has increased dramatically over the last few centuries. This growth clearly cannot continue forever; there must be upper limits on the total amount of energy that humanity could possibly consume. This discussion usually centers around the availability of resources, the technological means of power generation, and environmental sustainability.

Let’s imagine that these practicalities have been solved. Just for fun, we’ll enter a fantasy world where our ability to produce energy is unlimited; or more specifically, or ability to produce energy will continue to grow at the same rate as it did over the last century. Here’s the key question: how long could current growth rates continue before we hit an unstoppable thermodynamic limit?

This question was addressed in a recent article by Tom Murphy of the University of California. Tom used historic energy consumption data from the United States to extrapolate forward in time. I thought that it would be interesting to do something similar with global data.

After a quick web search, I had found two sources: a paper by Krausmann *et al* and the Statistical Review of World Energy published by BP. The BP review has data from 1965, whereas the Krausmann *et al* data begins in 1900. Here’s a graph:

The data indicate an exponential growth over the last century. How far back in history does the exponential growth extend? I only found data for the United States:

Nevertheless, I think that the trend is clear. It’s not too much of a stretch to imagine that humanity as a whole has benefited from at least 350 years of exponential growth in energy consumption. In those 350 years, our energy budget has increased by something like 4 orders of magnitude. The ready availability of all this energy has brought us so many things that we take for granted today. Our lives – in the wealthy countries at least – are made much more comfortable and (hopefully) enriching because of all of this energy.

Of course, the world population has also increased, so a fairer comparison is the per-capita energy budget:

I find this graph particularly interesting. Presumably, the end of the Second World War released some pent-up economic capacity, driving a huge increase in per-capita energy consumption. However, why is there a plateau around 1970 - 2000? What happened in 2000 that apparently kicked off another decade of rising consumption? These are some interesting questions, but I don’t want to get into them today.

Let’s get back to the fantasy of unabated growth. The last 350 years have seen exponentially increasing energy consumption. **What if this continues for another 350 years?** What would society look like?

Let’s take the trendline from the first figure and extrapolate.

In 350 years, if the present growth rate continues, human energy consumption will be comparable with the total amount of solar energy incident upon the Earth. That purple line represents the absolute upper bound on the amount of renewable energy that would be available to us without leaving the Earth. Any consumption above this line would necessarily be non-renewable, except if we build massive solar collectors in space.

Massive solar collectors in space sure do sound amazing, but there’s a problem. The total solar energy incident upon the Earth is equal – within a very good approximation – to the amount of energy escaping from the Earth. If there were not a balance between the two then the temperature of the planet would be changing. Of course, the balance is not exactly perfect, because the temperature of the Earth is changing, but the key point is that the purple line on the above graph tells us the Earth’s ability to dissipate heat into space, and therein lies the problem.

Any energy consumption above the purple line would add more heat to the planet than the sun does. How’s that for a thermodynamic limit? There is no way that we could live on a planet with that much extra heat. Regardless of the source of the energy, if our consumption were above the purple line then we’d be in trouble. It is the absolute upper limit on the amount of energy an Earth-bound civilisation could consume. There’s no way around this, because the vast majority of energy gets turned into heat when it is used. This heat is dispersed around the planet in all of the places where energy is consumed.

If the current energy growth continues, we’ll cross over the limit of one sun in 369 years, around 2383. That is not an inconceivable timeframe. The exponential growth has continued for 350 years so far, so another 369 is at least a little bit plausible. We’ll just have to operate our energy-intensive equipment off-planet.

Here are some other ways to look at this extrapolation. Our current energy consumption will double in 28 years. A child who is born today that lives until the age of 94 will witness an order of magnitude change in energy usage. An order of magnitude! The last order of magnitude change (from 1920 to today) brought about the invention or popularisation of virtually every electronic device ever created. What would another order of magnitude bring?

Certainly we live in interesting times. Can this growth really continue? Obviously it must stop eventually, but the question is when? Can we solve the technological and environmental problems? Let’s hope that we are up to the challenge.