**Does Life On Earth Violate
the Second Law of Thermodynamics?**

The second law of thermodynamics (the law of increase of entropy) is sometimes used as an argument against evolution. Evolution, the argument goes, is a decrease of entropy, because it involves things getting more organized over time, while the second law says that things get more disordered over time. So evolution violates the second law.

There are many things wrong with
this argument, and it has been discussed *ad infinitum*. A summary of the
arguments on both sides can be found on the links at www.talkorigins.org/faqs/thermo.html.
These discussions never seem to involve any numerical calculations. This is
unfortunate, since a very simple calculation shows that it is physically
impossible for evolution to violate the second law of thermodynamics.

It is important to note that the
earth is not an isolated system: it receives energy from the sun, and radiates
energy back into space. The second law doesn't claim that the entropy of *any
part* of a system increases: if it did, ice would never form and vapor would
never condense, since both of those processes involve a decrease of entropy.
Rather, the second law says that the *total* entropy of the *whole
system *must increase. Any decrease of entropy (like the water freezing into
ice cubes in your freezer) must be compensated by an increase in entropy
elsewhere (the heat released into your kitchen by the refrigerator).

A slightly more sophisticated
form of the anti-evolution argument recognizes that the earth is not an
isolated system; it receives energy from the sun. But, the argument goes on,
the sun's energy only *increases* disorder. It speeds the processes of
breakdown and decay. Therefore, even with an energy source, evolution still
violates the second law.

For the earth, though, we have to
take into account the change of entropy involved with *both* the
absorption of energy from the sun *and* the radiation of energy into
space. Think of the sun as a heat reservoir that maintains a constant
temperature T_{1} = 6000 K. (I am using the absolute, or Kelvin,
temperature scale.) That's the temperature of the radiating surface of the sun,
and so it's the effective temperature of the energy we receive from the sun.
When the earth absorbs some amount of heat, *Q*, from this reservoir, the
reservoir loses entropy:

_{}.

On average, the earth's
temperature is neither increasing nor decreasing. Therefore, in the same time
that it absorbs heat energy *Q* from the sun's radiation, it must radiate
the same amount of heat into space. This energy is radiated at a much lower
temperature that is approximately equal to the average surface temperature of
the earth, *T*_{2} = 280 K. We can think of space as a second heat
reservoir that absorbs the heat *Q* and consequently undergoes an entropy
increase

_{}.

Since *T*_{1} is
much larger than *T*_{2}, it is clear that the net entropy of the
two reservoirs increases:

_{}

Even if it is true that the
processes of life on earth result in an entropy decrease of the earth, the
second law of thermodynamics will not be violated unless that decrease is larger
than the entropy increase of the two heat reservoirs. Any astronomy textbook
will tell you that the earth absorbs 1.1 x 10^{17} Joules per second of
power from the sun, so in one year we get (1.1 x 10^{17} J/sec)x(365
days/year)x(24 hours/day)x(60 min/hr)x(60 sec/min) = 3.5 x 10^{24}
Joules of energy from the sun. This corresponds to an entropy increase in the
heat reservoirs of

_{}

Just how big is this increase? For comparison, let's calculate the entropy change needed to freeze the earth's oceans solid. The heat energy involved is

*Q *=
(latent heat of fusion)x(mass of ocean water) =

_{}

Water freezes at 273 K on the absolute scale, so the corresponding entropy change is

_{}

Comparing with the entropy
increase of the two heat reservoirs, we see that this is a factor of (1.6x10^{24}
J/K)/(1.2x10^{22} J/K) = 140
larger. Remember, though, that the number for the heat reservoirs was for one
year. Each year, more entropy is generated. The second law will only be
violated if all the oceans freeze over in about 140 years or less.

Now, the mass of all the living
organisms on earth, known as the *biomass*, is considerably less than the
mass of the oceans (by a very generous estimate, about 10^{16} kilograms.
If we perform a similar calculation using the earth's biomass, instead of the
mass of the oceans, we find that the second law of thermodynamics will only be
violated if the entire biomass is somehow converted from a highly disorganized
state (say, a gas at 10,000 K) to a highly organized state (say, absolute zero)
in about a month or less.

Evolutionary processes take place over millions of years; clearly they cannot cause a violation of the second law.

This article is adapted from my notes for Mr. Tompkins Gets Serious: The Essential George Gamow.

Check out my book, The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics.

© 2006 Robert N. Oerter