## INTRODUCTION

Pseudoscientists love to use "abracadabra" words to dazzle an ill-informed audience, and for creationists, the word "entropy" fills the bill nicely. The Second Law of Thermodynamics states that, in an isolated system, the entropy tends to increase. As entropy may be considered a measure of disorder, the orderliness of living systems and the complexity of organic molecules are taken by creationists to be a violation of this law of physics, requiring divine intervention.

An example of this sort of thinking is provided by Henry Morris (1989: 32, emphasis in the original):

The universe isnot"progressing from featurelessness to states of greater organization and complexity," as Davies and other evolutionary mathematicians fantasize. It is running down -at every observable level- toward chaos, as stipulated by the scientific laws of thermodynamics. Local and temporary increases in complexity are only possible when driven bydesignedprograms anddirectedenergies, neither of which is possessed by the purely speculative notion of vertically-upward evolution.

An even less intellectual effort is provided by Ross (2004: 108):

One feature of the law of decay (the second law of thermodynamics, or the entropy law) seems especially beneficial in the context of sin: the more we humans sin, the more pain and work we encounter.

Thank God for torture chambers, and congenital diseases!

A perfectly adequate response to such nonsense is to point out that the earth is not an isolated system, and therefore the condition required by the Second Law is not met. We can surely say more than just this, however. After all, entropy is not merely some nebulous concept of disorder, but an exactly defined quantity in physics. For example, 18 grams of water at 25° C has an entropy of 70.0 Joules per Kelvin (Lide 2004-5: 5-18; 6-4). Since entropy can be calculated precisely, it is possible to determine what restrictions the laws of thermodynamics really place on evolution. To do this, we should first look at how entropy is defined mathematically.

## THE CALCULATION OF ENTROPY

The change in the entropy of a system as it goes from an initial state to a final state is

ΔS = ∫ | dQ |

T |

which simplifies to

ΔS = | Q |

T |

if the temperature is constant throughout the process. In this equation:

S is the entropy in units of Joules per Kelvin (or J/K),

ΔS is the change in the entropy during the process,

Q is the flow of heat in units of Joules (or J) (Q is positive if heat flows into the object, and negative if heat flows out of the object), and

T is the temperature in units of Kelvin (or K).

For example, suppose that two cubes of matter at temperatures of 11 K and 9 K are brought together, 99 Joules of heat spontaneously flow from the hotter to the colder cube (as shown), and the cubes are separated. If the heat capacities of the cubes are so large that their temperatures remain essentially constant, the change in entropy of the entire system is

ΔS = | Q_{colder} |
+ | Q_{hotter} |
= | 99 | + | -99 | = 11 - 9 = +2 J/K. |

T_{colder} |
T_{hotter} |
9 | 11 |

Notice that this change of entropy is a positive quantity. The entropy of any system tends to increase, as energy flows spontaneously from hotter to colder regions.

## THE ENTROPY OF SUNLIGHT

To examine the change of entropy necessary to generate life on earth, begin with a square, one meter long on each side, at the same distance from the sun as the earth (93 million miles) and oriented so that one side fully faces the solar disk. The amount of radiant power that passes through this area is called the solar constant, and is equal to 1373 Joules/second (Lide 2004-5: 14-2). In the absence of the earth's atmosphere, the entropy of this sunlight would equal this energy divided by the temperature of the sun's surface, known from spectroscopy to equal 5780 K. The result would give the entropy of this amount of sunlight as 0.238 J/K every second.

A more sophisticated analysis of the energy and entropy that reaches the surface of the earth is given by Kabelac and Drake (1992: 245). Due to absorption and scattering by the atmosphere, only 897.6 J of energy reaches one square meter of the earth's surface through a clear sky every second (731.4 J directly from the solar disk, and 166.2 J diffused through the rest of the sky). For an overcast sky, all the energy is from diffuse radiation, equal to 286.7 J, according to Kabelac and Drake's model. The entropy that reaches this square meter through a clear sky every second is 0.305 J/K (0.182 J/K directly from the solar disk, and 0.123 J/K diffused through the rest of the sky). For an overcast sky, all the entropy is from diffuse radiation, equal to 0.218 J/K (see figure, p 32).

So, for one square meter on the earth's surface facing the sun, the energy received every second from a clear sky is 897.6 J, and the entropy received is 0.305 J/K. If we are to apply these numbers to a study of life on earth, we must spread these quantities over the entire earth's surface (of area 4πr^{2}) rather than the cross-section of the earth (of area πr^{2}) that receives the rays perpendicular to the surface. Therefore, these numbers must be reduced by a factor of 4 to represent the energy and entropy that an average square meter of the earth receives every second, as 224.4 J and 0.076 J/K, respectively.

## THE ENTROPY BUDGET OF ONE SQUARE METER OF LAND

The average temperature of the earth's surface is 288 K (= 15° C = 59° F) according to Lide (2004-5: 14-3). To maintain this temperature, that one square meter must radiate 224.4 J of energy back into the atmosphere (and ultimately into outer space) every second. The entropy of this radiation is

ΔS = | Q | = | 224.4 | = 0.779 J/K. |

T | 228 |

Assuming sunny skies, this one square meter of ground gains 0.076 J/K of entropy every second from sunlight, and produces 0.779 J/K every second by radiating energy back into the sky for a net entropy creation rate of 0.703 J/K every second. In effect, the earth is an entropy factory for the universe, taking individual high-energy (visible) photons and converting each of them into many low-energy (infrared) photons, increasing the disorder of the universe. As long as life on earth decreases its entropy at a rate of 0.703 J/K or less per square meter every second, the entropy of the universe will not decrease over time due to this one square meter of earth, and the Second Law will be obeyed.

How much energy and entropy are contained in life on the earth's land surface, compared to a lifeless earth? The average biomass occupying one square meter of land is between 10 and 12 kg, mostly as plant material (Bortman and others 2003: 145). Taking 11 kg as an average,we can calculate how much energy it would take to create this biomass from simple inorganic chemicals. This can be done by reversing the process, and asking how much energy is released when combustion reduces plant life to ashes. The answer is the heat of combustion, which for wood (which we may take as representative of plant life) is 1.88 x 10^{7} J/kg (Beiser 1991: 431). Multiplying these two numbers together, the energy required to generate the amount of life currently found on an average square meter of land is 2.07 x 10^{8} J.

If this life is generated at the earth's average temperature of 288 K, its entropy decrease will be

ΔS = | Q | = | 2.07 x 10^{8} |
= 7.18 x 10^{5} J/K. |

T | 228 |

The earth's bodies of water are relatively sterile, and can be ignored; if life on land can be generated, the sparse amount of life in water can certainly be generated as well.

## WHAT THE LAWS OF THERMODYNAMICS TELL US

We are now able to determine what restrictions the laws of thermodynamics place upon the evolution of life on earth. According to the First Law of Thermodynamics, heat is a flow of energy and must obey the Law of Conservation of Energy. The average square meter of land surface on earth receives 224.4 J of energy from the sun every second, and contains

2.07 x 10^{8} J of energy stored in living tissue. The ratio of these two values is

2.07 x 10^{8} |
= 9.22 x 10^{5} seconds = 10.7 days. |

224.4 |

If all the solar energy received by this square meter is used to create organic matter, a minimum of 10.7 days is required to avoid violating the First Law of Thermodynamics. The Second Law of Thermodynamics states that in an isolated system, the entropy tends to increase. The average square meter of land may balance the entropy increase due to radiation by generating a maximum entropy decrease of 0.703 J/K every second through the growth of life without violating this law. The difference in entropy between this square meter with life and the same square meter in the absence of life is 7.18 x 10^{5} J/K. The ratio of these two values is

7.18 x 10^{8} |
= 1.02 x 10^{6} seconds = 11.8 days. |

0.703 |

A minimum of 11.8 days is required to avoid violating the Second Law of Thermodynamics.

The Third (and final) Law of Thermodynamics, which states that S = 0 J/K for a pure perfect crystal at 0 K, has no application to creationism.

## CONCLUSION

Shades of a Creation Week! As long as the evolution of life on earth took longer than 10.7 or 11.8 days, the First and Second Laws of Thermodynamics are not violated, respectively. Even for an overcast sky, these numbers increase to merely 33 and 43 days respectively. As evolution has obviously taken far longer than this, the creationists are wrong to invoke entropy and the laws of thermodynamics to defend their beliefs.

Of course, solar energy is not going to be converted into the chemical energy of organic compounds with 100% efficiency. It takes a growing season of several months to reestablish the grasses of the prairie, and forests can take centuries to regrow. What this study has shown is that the time constraints for these two laws are very similar. Can creationists seriously argue that there has not been enough time for the sun to provide the energy stored in the living matter we find on earth today? If not, then they cannot honestly rely on entropy and the Second Law of Thermodynamics to make their case, either.