The Thermodynamic Argument Dismantled

In putting forward the ideas of Zero Waste in these pages, there is a subset of those who oppose those ideas who have enough scientific education to be able to turn to the science of heat and energy and quote the 2nd Law of Thermodynamics. This is a slippery and problematic law with many statements and definitions in conventional thermodynamics. all of which are usually shown to amount to the same thing. But one of the cogent statements is this:
The entropy of a closed system always increases if it changes at all. Alternatively: The entropy of a closed system never decreases.

In order to appreciate the philosophical meaning of this statement, you need to know that entropy has been proven to be equivalent to disorder. The more ways there are to arrange the parts of a system, the higher the entropy. If all the parts have to be in rigidly ordered relationships to each other, such as when a material is at absolute zero so the molecules hardly move, then there are very few arrangements and entropy is low. As systems are shaken or absorb heat and exchange heat and as the molecules move around, the disorder always increases. Molecules never spontaneously drop into an organized alignment. We must work on them somehow to make that happen. When water molecules in ice, which are fairly rigidly kept in place, are given heat and change to liquid water, where the molecules can now move around, the entropy of the water increases.

The reason for bringing this up is that people assume that an increase in entropy means losing control of where everything goes and that means the creation of waste. Thus Zero Waste cannot succeed. As fast as you try to cram some waste back into a useful form in one place, so the argument goes, you create even more waste somewhere else by your actions. At least that is the claim.

The claim immediately fails on its face. The 2nd Law applies to a closed system. A system that exchanges either heat or energy or materials with its outside environment is not closed, it is open. The earth is bathed in a huge amount of incoming energy in the form of radiation from the sun. The earth is an open system to which one cannot apply the 2nd Law. Combining the earth with the sun would be closer to a closed system but in that case, the sun is undergoing a huge increase in entropy compared to the earth (since the sun processes huge amounts of materials and energy every second) which completely overwhelms any small effect we might indulge in on the earth. So Zero Waste is perfectly possible if we can make use of the sun’s energy to control terrestrial processes so that no waste is produced.

This then is the outline of the analysis. But can we put numbers to this to make sure that the entropy increase due to the sun is truly much greater than anything possible on earth?

At this point, those who have never studied thermodynamics might want to bow out and return to blog reading. However I have provided a reasonably clear explanation of the Thermodynamics you need to know.

Entropy change is fundamentally defined as the amount of heat that enters a system divided by the temperature of the system. This is not an exact definition, as can be seen from the phrase “the temperature”. The system should change slowly enough so that it is all at one temperature, but for a rough calculation we will ignore this fine point and assume we know average temperatures and the system stays in thermal equilibrium.

ΔS = ΔQ/T

Where S is the entropy, Q is the amount of heat in any convenient units and T is the absolute temperature. It is not Centigrade but Centigrade plus 273, called the Kelvin temperature and represented by K. Δ means an amount of change. In this convention, when heat enters, it is positive and the entropy increases. When heat leaves, it has a negative sign and the entropy decreases.

I am indebted to Robert Oerter for this calculation. His website answers a related question: does life and evolution on earth violate the 2nd Law?

Oerter’s assumption is that the sun delivers a certain amount of heat to the earth. It also delivers a far greater amount of heat to the solar system and the universe but that heat, which implies an even greater change in entropy, does not end up in the earth and so cannot be said to offset the terrestrial increase. Therefore, let us take only the heat which falls on the earth’s surface and recognize that it leaves the sun at a high temperature and arrives on earth at a low temperature.

The amount of heat hitting the earth in the form of radiation is known as the albedo and it is a figure that has been estimated in many ways. Any astronomy textbook will tell you that the earth absorbs 1.1 x 1017 Joules per second of power from the sun, so in one year we get (1.1 x 1017 J/sec)x(365 days/year)x(24 hours/day)x(60 min/hr)x(60 sec/min) = 3.5 x 1024 Joules of energy from the sun.

Think of the sun as a heat reservoir that maintains a constant temperature T1 = 6000 K. The surface temperature of the earth can be taken to be 300 deg K., 20 times lower.

The sun’s loss of entropy for the heat that arrives on earth is 3.5 x 1024/6000 =approximately 5 x 1020 J/deg. while that same amount of heat striking the earth at an average temperature of 300 deg K adds 3.5 x 1024/300= approx. 1 x 1022 J/deg./year which is 20 times larger due to the lower temperature. Since heat always moves from a high temperature to a low temperature body, as here, the entropy of the combined system always increases upon the transfer of heat.

So now we have big, annual numbers, but what do they mean? To put them into a context, we need to make a comparison to something that might be related to the amount of human industrial activity carried out in one year. I will use the combustion of all the crude oil extracted from the ground in a typical year. The internet quickly yields a number of about 70 million barrels of oil used worldwide per day in recent days. Multiply that by 365 days per year and then by 54 gallons per drum and 3 kilograms per gallon and we get:

4 x 1012 kg oil/year worldwide

The combustion of petroleum yields approximately 11 million calories per kg. or about 50 million joules per kg. Multiply these together and we get an energy output from burning all the oil used in the world in one year to be 2 x 1020 joules. If we very crudely assume that this heat enters our biosphere at 300 deg K, the annual entropy gain from burning oil is 6 x 1017 joules/deg K.

Compare this to the 1 x 1022 joules/deg K. coming in from the sun annually. The entropy contributed by the sun is over ten thousand times larger.

What this means is this: if we capture a tiny fraction of the energy streaming in from the sun in a coherent form like electricity (not contributing directly to entropy increase) instead of letting it be absorbed into heat, and use that electricity to do work on the far smaller entropy increase from human processes, we can transform those processes into waste-free forms and never affect the energy and entropy balances of our planet to any noticeable extent.

QED

 

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