Another Error about Thermodynamics
Immediately after the words cited above, Brush says:
A better response is to point out that the equilibrium state of a system is determined by seeking not the maximum entropy but the minimum free energy; which balances energy against entropy (E–TS). An obvious example is the crystallization of water molecules from a vapor: at low temperatures a low-energy state with low entropy (a crystal) will be favored over a high-energy state with high entropy (a gas). The Creationist version of thermodynamics fails to explain why it snows.[i]
[i] Ibid.
Brush reaches wrong conclusions because he omits careful analysis before pressing the point he wants to make. First let us explain equilibrium. If a car is left with brakes off and its transmission in neutral at the top of a hill, the car is not in equilibrium. A small push will make it roll to the bottom of the hill. But if the car is left in the same condition at the bottom of the hill then it is in equilibrium. A small push may make it roll back and forth a little, but it will settle at the bottom. What makes the difference? At the top of the hill the car has potential energy that a small push can release. We may call this potential energy “free energy” because it can be freed. At the bottom of the hill the potential energy is much less. The free energy is minimal, that is, it goes to zero, when the system (the car on the hill) is in equilibrium.
Let us now consider a cloud containing tiny, suspended ice crystals. In the cloud water vapor is in direct contact with ice. What will happen depends on the conditions.
Over a range of temperatures, if pressure is exactly right for the temperature, the ice will not melt and the water vapor will not freeze. This is what we call equilibrium. At equilibrium the water vapor is at the same temperature as the ice. There can be no flow of heat if there is no difference in temperature. At any constant temperature the entropy change of the water vapor is the heat that flows out divided by the absolute temperature. At equilibrium no heat flows out, so the entropy change of the water vapor is zero. The entropy change of the ice is also zero for the same reason. The tiny ice crystals remain suspended in the cloud. They do not grow, so they never become big enough to fall out of the cloud. There will be no snow as long as the temperature and pressure remain right for each other to establish equilibrium. Specialists in thermodynamics can calculate the pressure right for the temperature using the known properties of ice and water vapor. From these they calculate the free energy, and identify the temperature and pressure that will minimize the free energy. Let us take careful note that the minimum free energy tells us the pressure and temperature that will not produce snowfall and will not lead to any increase of entropy.
If snow is in fact forming then the water vapor and ice are not in equilibrium. Something must be cooling the cloud to lower its temperature enough for water vapor to freeze. Usually a cloud cools when an updraft forces it upward to the cooler regions of the upper atmosphere. Whenever there are winds there is an increase of entropy, because winds are not reversible.
Cooling is necessary to produce snowfall. Consider what happens between the water vapor molecules and the suspended ice crystals. There will always be a distribution of speeds among the water vapor molecules. Some will be moving faster than others. If a fast-moving molecule hits an ice crystal it is likely to bounce off, but a slowly moving molecule may stick and make the crystal grow. Removing the slowly moving water vapor molecules from the cloud and sticking them on the crystals makes the average speed of the remaining water vapor molecules faster. Since the average speed is faster, the remaining water vapor warms up. A temperature difference arises between the water vapor and the ice crystal. This seems contrary to the second law of thermodynamics. When a hot stone falls into cold water both come to the same temperature, but now it seems that a cool molecule landing on ice makes the remaining water vapor heat up. Is this in fact a contradiction? No, the second law of thermodynamics talks about the initial and final states of a system, and of regions “containing a number of molecules sufficiently large for microscopic fluctuations to be negligible.”[i] There can be fluctuations around the equilibrium. If the water vapor heats up because the slowest molecules stick to the ice, the additional heat in the water vapor will flow back into the ice and melt some of it. That will replace the water vapor molecules lost when they stuck to the ice. However, if something cools the cloud, it will take away the extra heat of the faster molecules that remained in the vapor state when the slowest molecules stuck to the ice. Cooling allows the slowest of the remaining vapor molecules to keep on sticking to the ice, making the ice crystals grow, form snow, and fall out of the cloud.
Brush is confused by the fact that the entropy in a changing system always increases (goes to a maximum) but the free energy is minimum when there is equilibrium (when the system is not changing). Enrico Fermi (Italian-born American physicist, 1901–1954) analyzed the free energy clearly and simply in his classic book Thermodynamics.[ii] It is preposterous to imagine that Fermi knew that every snowfall violates the second law of thermodynamics. Fermi mentions no exceptions to the second law and Einstein said that the laws of thermodynamics are of universal application. The argument that crystallization contradicts the second law apparently circulated long before Brush wrote his article. However, the argument has no basis in physics. It is simply wrong. The only reason for its persistence appears to be uncritical thinking on the part of people who don’t really understand thermodynamics. Uncritical thinking prevails especially when people are afraid, for example, when precision science threatens their favorite speculation.
[i] Prigogine, op. cit. pp. 15–18.
[ii] Fermi, Enrico, Thermodynamics (New York: Dover, 1936), §17, pp. 77–82.
Let us now consider a cloud containing tiny, suspended ice crystals. In the cloud water vapor is in direct contact with ice. What will happen depends on the conditions.
Over a range of temperatures, if pressure is exactly right for the temperature, the ice will not melt and the water vapor will not freeze. This is what we call equilibrium. At equilibrium the water vapor is at the same temperature as the ice. There can be no flow of heat if there is no difference in temperature. At any constant temperature the entropy change of the water vapor is the heat that flows out divided by the absolute temperature. At equilibrium no heat flows out, so the entropy change of the water vapor is zero. The entropy change of the ice is also zero for the same reason. The tiny ice crystals remain suspended in the cloud. They do not grow, so they never become big enough to fall out of the cloud. There will be no snow as long as the temperature and pressure remain right for each other to establish equilibrium. Specialists in thermodynamics can calculate the pressure right for the temperature using the known properties of ice and water vapor. From these they calculate the free energy, and identify the temperature and pressure that will minimize the free energy. Let us take careful note that the minimum free energy tells us the pressure and temperature that will not produce snowfall and will not lead to any increase of entropy.
If snow is in fact forming then the water vapor and ice are not in equilibrium. Something must be cooling the cloud to lower its temperature enough for water vapor to freeze. Usually a cloud cools when an updraft forces it upward to the cooler regions of the upper atmosphere. Whenever there are winds there is an increase of entropy, because winds are not reversible.
Cooling is necessary to produce snowfall. Consider what happens between the water vapor molecules and the suspended ice crystals. There will always be a distribution of speeds among the water vapor molecules. Some will be moving faster than others. If a fast-moving molecule hits an ice crystal it is likely to bounce off, but a slowly moving molecule may stick and make the crystal grow. Removing the slowly moving water vapor molecules from the cloud and sticking them on the crystals makes the average speed of the remaining water vapor molecules faster. Since the average speed is faster, the remaining water vapor warms up. A temperature difference arises between the water vapor and the ice crystal. This seems contrary to the second law of thermodynamics. When a hot stone falls into cold water both come to the same temperature, but now it seems that a cool molecule landing on ice makes the remaining water vapor heat up. Is this in fact a contradiction? No, the second law of thermodynamics talks about the initial and final states of a system, and of regions “containing a number of molecules sufficiently large for microscopic fluctuations to be negligible.”[i] There can be fluctuations around the equilibrium. If the water vapor heats up because the slowest molecules stick to the ice, the additional heat in the water vapor will flow back into the ice and melt some of it. That will replace the water vapor molecules lost when they stuck to the ice. However, if something cools the cloud, it will take away the extra heat of the faster molecules that remained in the vapor state when the slowest molecules stuck to the ice. Cooling allows the slowest of the remaining vapor molecules to keep on sticking to the ice, making the ice crystals grow, form snow, and fall out of the cloud.
Brush is confused by the fact that the entropy in a changing system always increases (goes to a maximum) but the free energy is minimum when there is equilibrium (when the system is not changing). Enrico Fermi (Italian-born American physicist, 1901–1954) analyzed the free energy clearly and simply in his classic book Thermodynamics.[ii] It is preposterous to imagine that Fermi knew that every snowfall violates the second law of thermodynamics. Fermi mentions no exceptions to the second law and Einstein said that the laws of thermodynamics are of universal application. The argument that crystallization contradicts the second law apparently circulated long before Brush wrote his article. However, the argument has no basis in physics. It is simply wrong. The only reason for its persistence appears to be uncritical thinking on the part of people who don’t really understand thermodynamics. Uncritical thinking prevails especially when people are afraid, for example, when precision science threatens their favorite speculation.
[i] Prigogine, op. cit. pp. 15–18.
[ii] Fermi, Enrico, Thermodynamics (New York: Dover, 1936), §17, pp. 77–82.