# A Barrel of Crude Oil is Worth \$164,000 – The Human Labor Equivalent of a Barrel of Oil

Posted on April 30, 2011 I heard that in a single barrel of oil there is the energy equivalent of 23,000 human labor hours.  This amounts to 12 years (40 hours per week) if vacations are factored in, so…

A single barrel of oil can do what it would take me 12 years to do working with my hands?

If this is true, oil is essentially “free” energy at the current price.  I decided to check it out, as the claim seemed a little hard to believe at first.

After some quick calculations from first principals (see below), I found that for a purely theoretical task, like heating water with a pedal powered generator, the claim is correct.  It would indeed take 12 years of laboring to produce the same amount of heat energy as a single barrel of oil.

For a task that involves producing mechanical energy, I made (what I consider to be) some reasonable assumptions and found that a human would take about 3 years to do what a single barrel of oil can do working via a typical internal combustion engine.

Now if a person is getting paid a fair amount per hour (and allowing for vacation time in all the calculations) I conclude that….

The Human Labor Equivalent of a Barrel of Oil is \$164,000 USD

For further reading there is a is a fascinating discussion on the OILDRUM that looks at this issue from a number of different angles [here].  My own discussion, which is also a refresher of some basic physics and explains how I got to my answer follows in the next section.

When all the oil is gone, if we haven’t found a suitable replacement, the human value of labor will again become apparent…

Will enforced slavery make a big comeback?

How extreme will the wars rage for the last few available drops?

How many of our children’s children will suffer because we were not better stewards?

.

.

Crude Oil \$164,000 a Barrel – it’s not that far off the mark!

# Work – Heat Conversion Theory

In this context we are talking about mechanical work that I can do with my hands (12 years worth) – but we all know intuitively that the energy stored in a barrel of oil is chemical energy (or heat energy after you set it on fire) – how can you convert between the two figures in a meaningful way…?

In 1845 a guy called Joule wrote a paper called the “mechanical energy of heat” where he found that a falling weight of 1 pound had to fall a distance of 772.24 ft to produce an increase in temperature (in 1 pound of water) of 1 degree Fahrenheit – the weight to distance relationship could be any other combination that multiplies out to 772.4lb.ft – for instance a 772.4lb  weight falling 1 foot or a 386.2lb weight falling 2 feet for example.

The SI unit of mechanical work is called the Joule in honor of the man who made up this experiment.  A Joule is equal to 1 Newton of force applied on an object for a distance of 1 meter.

Work (Joules) = Force (Newtons) x Distance (Meters) and where

Force (Newtons) = mass (kilograms) x acceleration due to gravity (9.81 m/s^2)

Some necessary conversion factors before we go any further –

1 pound = 0.45359237 kilograms

1 foot = 0.3048 meters

So converting the experiment that Joule did back to SI units, I first need to work out the number of Newtons force that were used in the original experiment:

Force (Newtons) =  0.45359237 kilograms/lb x 772.4lb x 9.81 m/s^2 = 3,437 N

And force worked over 1 ft of distance (.3048m) so

Work (Joules) = 3.437N x 0.3048m = 1047.6 Joules

So we have in the original experiment, 1047.6 Joules of Energy needed to raise 1lb of water by 1 degree Fahrenheit.  Since I am going to work everything back to SI units, I need to scale the experiment so we have the water quantity 1kg, and a change in temp of 1 degree Celsius (the standard SI Units).

1 degree interval change in Celsius scale (the SI Unit) represents a 1.8 degree change on the Fahrenheit scale (the original experiment), so need to scale up:  1047.6 x 1.8 = 1,885.68 Joules / lb of water.

Because a pound of water is smaller than a one Kg, we need to scale up again with regards to the quantity of water involved so we have 1,885.68 / 0.4536 = 4,157.

So we need to apply 4,157 Joules of work to raise 1 Kg of Water By one Degree C.

This experiment leads to the concept of specific heat of water – lets consider a gram of water (1/1000 of a kg).  The mechanical force required to heat this up (as per joules experiment) is 4.16 Joules (actually the figure is 4.18 after applying correct rounding factors).  Or to put it another way, 4.18 Joules of mechanical energy are required to raise a gram of water by 1 degree or… 4.18 Newtons force pushing for 1 meter distance will raise a gram of water by 1 degree or…  OR, 4.18 Joules of heat energy (Say from burning few drops of crude oil) will heat up a gram of water by 1 degree.

Now there are many thousands of drops of crude oil in a barrel of crude – and in fact we know that…

in a barrel of oil there are 6.1E9 Joules of heat energy*

(*energynumbers.pdf) or 6,100,000,000 Joules or 6.1 Billion Joules. Checking some figures back then into real world terms, by asking how much water can a barrel of crude heat up? I divide the above figure by 4.18, and find I can raise the temp of 1459330144 grams of water by 1 degree with a barrel of crude, or 1,459 cubic meters of water by one degree, or 29.2 cubic meters of water by 50 degrees.  An average Olympic sized pool is 2,500m3 (x this volume by 1E6 to get grams) and divide by 1459330144…

A single barrel of crude oil can raise the temp of an Olympic Sized Swimming Pool by 1.7 Degrees Celsius

Now the abstract concept of a Joule (1 x unit force x 1 x unit distance) is  kind of meaningless in the real world – because the real world lives in the realm of time.

The concept of power needs to be introduced.  Power = Work Done / Time Taken.  That is to say, if I do a unit of work in a small amount of time, I must have applied more power to get this work done compared to if it had taken a long time.  Enter the concept of a unit of Power = 1 Watt = 1 Joule / Second. From the previous discussion, it should be obvious that…

4.18 Watts = 1 degree rise in 1 gram of water per second.

Back to the Barrel of oil.  Depending on how quickly we burn the barrel of oil, depends on how quickly we heat the water, if I burned the entire barrel in 1 second I would be producing power at 6.1E9 Watts or 6,100MW.  The Hydro Generation Scheme that I used to work on produces at a rate of about 1,000MW instantaneousness generation so effectively the scheme is producing the same amount of power as a barrel of oil does every 6.1 seconds.

Interestingly, 6,1000MW instantaneous (1 second) power, relates to about 1.7 MW.hours (divide by 60×60 to convert seconds to hours).  This unit of MW.hour is the same unit that electricity is traded in at a wholesale level, and is usually about \$100 give or take depending on which part of the world you are in.

A Thought Experiment

Now lets say I buy a machine that can convert human work into watts and I hook it up to heat my water at home.

There is actually a machine like this for sale on the internet [here] it costs about \$550 and can put out 65 Watts. It just so happens that a healthy human can sustain 75 Watts output for about 8 hours a day [reference].

Or to rephrase, a typical human can sustain about 75 Joules per second for days at a time.   Now to find out then how many hours of work there are in barrel of crude (for this simple task of heating water at least) we just divide 6.1 E9 Joules by 75 and we get ta daaaaaaa:

81333333 seconds = 1355555 minutes = 22592 hours = 564 (40 hour weeks) = 12 working years (about 48 working weeks in a year).

So the initial claim is correct, there is 12 years of work in a barrel of Oil! for this “Heating Water” type task.

It must also be noted that while mechanical energy can be converted to heat it is not possible to entirely convert heat into mechanical energy. This is one aspect of the second law of thermodynamics –  and this really needs to be kept in mind.

The picture at top shows a man carrying / dragging a rickshaw along the street.  Now he can work at about 75 Watts over the long term, but all the energy he produces does not go into forward motion, I am going to assume that he only converts about 50% of his power into forward motion. If he were riding a pedal cycle, the conversion of his power into motion would be much better, but my point is, even “smart” human labor can’t convert everything into useful work.  Likewise, the internal combustion engine is a very poor converter of heat energy into mechanical energy as the above diagram shows.  My second theoretical task is at hand, I am going to compare a rickshaw and an equally slow moving motorized vehicle –  for both the Rickshaw and the car I am going to ignore wind affects because the low travel speeds minimizes this affect as it also does for braking affects.  Going off the diagram above, the conversion of oil to forward or useful motion is then 12.6%.  This is going to compare to a massively more efficient human working at about 50% efficiency.

A barrel of oil will effectively convert 6.1E9 x .126 = 770E6 Joules of heat energy into useful motion.  Under my set of assumptions above, the human operating at 50% efficiency will by converting 75Watts x .05 = 37.5Watts.  So for my second theoretical task, a barrel of oil contains 770E6 / 37.5 =

20533333 seconds = 5,704 hours = 142 (40 hour weeks) = 3 Years of rickshaw pulling.

So there is 3 years of work in a barrel of Oil!  for this “Rickshaw” type task.

Now because this is my blog, I am going to assume a three more things:

1 – A fair rate to pay someone is about \$15 / hour actually worked USD as opposed to the dehumanizing type labor rates of \$1.50 per day that currently prevails for more than 15% of humanity.

2 – The ratio of heating to rickshaw type tasks is about 70 / 30 in favor of the rickshaw type of work.  This covers the fact that humans are always likely to have other sources of energy available to do basic heating type tasks, and also puts some weight on the fact that machines can do tasks that humans can’t easily do, like a 70 Ton excavator digging rock for instance.

3 – The working year is based on 48 weeks work at 40 hours a week (which is really still a little high to have full and balanced quality of life if you ask me).

So with these two figures in mind I am going to compute actual value of a barrel of oil.

3 years x .7 + 12 years x .3 = 5.7 years, at 40hours x 48 weeks and \$15 per hour…..

\$164,000 per barrel

Posted in: Green