ON THE FALLACIOUS APPEAL TO THE SECOND LAW OF THERMODYNAMICS
WHAT ARE ENTHALPY AND ENTROPY?
WHAT DOES THE 2ND LAW SAY?
THERE IS NO SUCH THING AS A “LOCAL VIOLATION” OF THE SECOND LAW
(continued)
(EDITED 15MAR06 to correct a boneheaded math error, and to refine the explanation)
We've all heard the argument that the Second Law says that the disorder of a system increases with time, so evolution can't be true because it would require a violation of physics. This argument is based on a basic misunderstanding, both of what entropy is, and of what the Second Law says and what it means. In this post, I will attempt to explain:
I believe that I'm qualified by training and experience to speak as an expert on this topic. I hold a Bachelor of Science Degree in Mechanical Engineering (Cum Laude) from a respected university, I got a 98+ in Thermodynamics (similar grades in physics, calculus and statistics), I have 14 years experience in the automotive industry, and I've thought about this a lot.
NOTE: as I post this I'm away from home on a work trip. I'm working about 14 hours a day for the next week or so and won't be able to make more than very brief replies. Thanks for your patience.
1. That, in thermodynamics, the word “entropy” is used to describe two distinct but related properties.
2. What the Second Law says and what it means.
3. That there is no such thing as a “local violation” of the Second Law.
4. That entropy is not a generic measure of disorder.
5. That the claim that entropy is a measure of spatial order leads to a violation of the Second Law.
6. That information has no thermodynamic entropy.
I want to clarify that I'm not making any comment about the merits of the theories of evolution or creation. I'm ONLY trying to explain why it's a poor tactic to use a Second Law argument in an attempt to refute evolution. Darwin’s psychology, the geologic record, the social fallout of evolutionary theory, the interpretation of Biblical texts, and anything else not directly related to thermodynamics are simply not relevant to this discussion. Also, if I say below that something is not possible, the comment is intended only to describe the normal behavior of the world, and is not a denial of God’s ability to do whatever He wants.2. What the Second Law says and what it means.
3. That there is no such thing as a “local violation” of the Second Law.
4. That entropy is not a generic measure of disorder.
5. That the claim that entropy is a measure of spatial order leads to a violation of the Second Law.
6. That information has no thermodynamic entropy.
I believe that I'm qualified by training and experience to speak as an expert on this topic. I hold a Bachelor of Science Degree in Mechanical Engineering (Cum Laude) from a respected university, I got a 98+ in Thermodynamics (similar grades in physics, calculus and statistics), I have 14 years experience in the automotive industry, and I've thought about this a lot.
NOTE: as I post this I'm away from home on a work trip. I'm working about 14 hours a day for the next week or so and won't be able to make more than very brief replies. Thanks for your patience.
WHAT ARE ENTHALPY AND ENTROPY?
Enthalpy is an intensive state property of matter, intensive meaning that its value is independent of the amount of matter present. Other intensive properties you may be more familiar with are density, coefficient of thermal expansion, and electrical conductivity. Enthalpy is a measure of the amount of internal heat of a substance; it is dependent on temperature and pressure, and is measured in units of Joules per kilogram.
The term “entropy” is used to describe two different but related properties of a thermodynamic system. In conversation, "entropy" is used interchangeably to describe both of these properties, with the context usually clarifying which meaning is intended.
In one sense, entropy is another intensive state property of matter, that being a measure of the ability of the internal heat of a substance to do work. Its value is expressed in units of Joules per kilogram-degree K, and is also dependent on temperature and pressure. At absolute zero, a a perfect crystal of an inert, non-radioactive substance has zero intensive entropy. If an atom solidifying onto a crystal doesn’t get into the correct position, then some of the heat of fusion of that atom is not released to the environment. If an otherwise perfect crystal is brought to absolute zero, its entropy is not exactly zero because there is some amount of heat energy still locked up and available to do work.
As temperature increases, so does the entropy of the substance. When the substance changes phase (such as when ice melts) its entropy changes even though its temperature does not. When you return the substance to its original pressure and temperature, it has the exact same value of entropy as it did at the beginning of the process. It is not uncommon to hear these kinds of entropy changes, which involve no violation of the Second Law, referred to as local changes in entropy; this unfortunate term should never be used as it leads to serious misunderstandings of the Second Law (as will be described below).
Total entropy is an extensive state property of thermodynamic systems, extensive meaning that its value is dependent on the amount of matter present. Total entropy is measured in units of Joules per degree K. Engineers are typically interested in changes in total entropy (sometimes referred to as entropy generation, shown by the symbol “dS”
during a process, since these changes are a direct measure of the efficiency of the process. Mathematically, the entropy generated by a process is given by the sum (Σ
of the energy transfer (dQ) divided by the temperature (T) of the elements the energy is flowing into: dS = Σ(dQ/T).
When modeling power generation or refrigeration systems, one rarely is concerned with the intensive entropy of the solid phase of the working fluid because solids cannot be easily pumped between the heat source and the heat sink. Because of this, it is common to assign a value of zero intensive entropy to the coldest temperature at which the working fluid is fluid in order to simplify the calculations. This is merely a convention, and in practice one may assign a value of zero to any convenient temperature. In the examples below I’ve assigned a value of zero to ice at temperature of 273 K (the freezing temperature), and calculated the values at the other states from standard tables of entropy (which can be found online using the search terms “steam tables entropy”
.
Let me provide a concrete example. Imagine a system of two masses of water, one a hot vapor and the other a cold block of ice. They are of just the right size so that the heat heat required to fully melt the ice is the exact amount required to fully condense the steam. The two masses are brought into contact just long enough to fully melt the ice and condense the steam. The entropy changes are as follows:
The steam has a mass of 1.0 kg, is at the vaporization temperature (373 K)and has intensive entropy of 15.9 kJ/kg*K. The heat flow out of the steam is 2257 kJ, which reduces the ability of the steam to do work (i.e., lowers its entropy). During this process the steam changes phase from a gas to a liquid without changing temperature, and at the end it has an intensive entropy of 9.6 kJ/kg*K. Thus the change in the intensive entropy of the steam is 9.6 - 15.9= -6.3 kJ/kg*K.
The ice has a mass of 6.8 kg, is at the freezing temperature (273 K) and has an intensive entropy of 0.0 kJ/kg*K. The heat flow into the ice is 2257 kJ (the same as the heat that came out of the steam),which increases the ability of the ice to do work (i.e., raises its entropy). During this process the cold mass changes phase from a solid to a liquid without changing temperature, and at the end it has an intensive entropy of 8.3 kJ/kg*K. Thus the change in the intensive entropy of the cold mass is 8.3 – 0.0= 8.3 kJ/kg*K.
The total entropy generated by this process is given by dS = (-2257/373) + (2257/273) = -6.3 + 8.3 = 2.0 kJ/K.
The energy present in a system is contained in both the free heat energy (what we’d measure as temperature), the chemical energy contained in the molecules of the substance, and the atomic energy contained within the atoms. In thermodynamic discussions it’s assumed that the chemical and atomic energy can be neglected unless one is specifically dealing with reacting systems. Reacting and radioactive systems are more complex to analyze but the basic rules are the same.
The term “entropy” is used to describe two different but related properties of a thermodynamic system. In conversation, "entropy" is used interchangeably to describe both of these properties, with the context usually clarifying which meaning is intended.
In one sense, entropy is another intensive state property of matter, that being a measure of the ability of the internal heat of a substance to do work. Its value is expressed in units of Joules per kilogram-degree K, and is also dependent on temperature and pressure. At absolute zero, a a perfect crystal of an inert, non-radioactive substance has zero intensive entropy. If an atom solidifying onto a crystal doesn’t get into the correct position, then some of the heat of fusion of that atom is not released to the environment. If an otherwise perfect crystal is brought to absolute zero, its entropy is not exactly zero because there is some amount of heat energy still locked up and available to do work.
As temperature increases, so does the entropy of the substance. When the substance changes phase (such as when ice melts) its entropy changes even though its temperature does not. When you return the substance to its original pressure and temperature, it has the exact same value of entropy as it did at the beginning of the process. It is not uncommon to hear these kinds of entropy changes, which involve no violation of the Second Law, referred to as local changes in entropy; this unfortunate term should never be used as it leads to serious misunderstandings of the Second Law (as will be described below).
Total entropy is an extensive state property of thermodynamic systems, extensive meaning that its value is dependent on the amount of matter present. Total entropy is measured in units of Joules per degree K. Engineers are typically interested in changes in total entropy (sometimes referred to as entropy generation, shown by the symbol “dS”
When modeling power generation or refrigeration systems, one rarely is concerned with the intensive entropy of the solid phase of the working fluid because solids cannot be easily pumped between the heat source and the heat sink. Because of this, it is common to assign a value of zero intensive entropy to the coldest temperature at which the working fluid is fluid in order to simplify the calculations. This is merely a convention, and in practice one may assign a value of zero to any convenient temperature. In the examples below I’ve assigned a value of zero to ice at temperature of 273 K (the freezing temperature), and calculated the values at the other states from standard tables of entropy (which can be found online using the search terms “steam tables entropy”
Let me provide a concrete example. Imagine a system of two masses of water, one a hot vapor and the other a cold block of ice. They are of just the right size so that the heat heat required to fully melt the ice is the exact amount required to fully condense the steam. The two masses are brought into contact just long enough to fully melt the ice and condense the steam. The entropy changes are as follows:
The steam has a mass of 1.0 kg, is at the vaporization temperature (373 K)and has intensive entropy of 15.9 kJ/kg*K. The heat flow out of the steam is 2257 kJ, which reduces the ability of the steam to do work (i.e., lowers its entropy). During this process the steam changes phase from a gas to a liquid without changing temperature, and at the end it has an intensive entropy of 9.6 kJ/kg*K. Thus the change in the intensive entropy of the steam is 9.6 - 15.9= -6.3 kJ/kg*K.
The ice has a mass of 6.8 kg, is at the freezing temperature (273 K) and has an intensive entropy of 0.0 kJ/kg*K. The heat flow into the ice is 2257 kJ (the same as the heat that came out of the steam),which increases the ability of the ice to do work (i.e., raises its entropy). During this process the cold mass changes phase from a solid to a liquid without changing temperature, and at the end it has an intensive entropy of 8.3 kJ/kg*K. Thus the change in the intensive entropy of the cold mass is 8.3 – 0.0= 8.3 kJ/kg*K.
The total entropy generated by this process is given by dS = (-2257/373) + (2257/273) = -6.3 + 8.3 = 2.0 kJ/K.
The energy present in a system is contained in both the free heat energy (what we’d measure as temperature), the chemical energy contained in the molecules of the substance, and the atomic energy contained within the atoms. In thermodynamic discussions it’s assumed that the chemical and atomic energy can be neglected unless one is specifically dealing with reacting systems. Reacting and radioactive systems are more complex to analyze but the basic rules are the same.
WHAT DOES THE 2ND LAW SAY?
The Second Law is a mathematical description of the behavior of total entropy during thermodynamic processes: “Every real thermodynamic process results in an entropy generation greater than or equal to zero”. Mathematically, this is given by the furmula “dS >/= 0 kJ/K”. Looking back to the ice and steam example above, see that the process resulted in a positive generation of entropy (+2.2 kJ/K)
Imagine a process in which heat flows from the cold water (causing it to freeze) into the hot water (causing it to boil). The entropy generation from that process would be -8.3 + 6.3 = -2.0 kJ/K, which would violate the Second Law, and in fact heat does not spontaneously flow from cold objects to hot ones.
There are several corollaries to the Second Law, one of which can be stated as follows: "In a closed system, total entropy increases for irreversible processes and remains constant for reversible processes". Irreversible processes are those that result in an increase in total entropy; such processes can only occur in one direction. For example, you can heat up a fluid by spinning a paddle in it, but you cannot apply the heat energy of a fluid to a paddle and make the paddle spin. You can heat two objects up by rubbing them together, but you cannot make two objects rub together by heating them up. Energy expended in irreversible processes is no longer available to do work, so it is referred to as being irreversibly lost.
Not all processes are irreversible. When you use a rotating shaft to raise a weight, you can harness all of the potential energy of the raised weight to make the shaft spin again. There is, therefore, no change in total entropy due to the work done in raising the weight. When you slowly pressurize a gas by moving a piston against it, you can recover all of the work done by allowing the piston to move back to its original position under the pressure of the gas. There is no change in total entropy when a gas is pressurized slowly, thus the process is completely reversible.
The entropy generation of a process is a measure of both the irreversibility and the efficiency of the process. If one compares two processes that perform the same amount of work, the process that generates the least total entropy is the least irreversible (the most reversible) and the most efficient.
Another corollary to the Second Law is "there can be no machine whose only effect is to cause heat to flow from a cold body to a warm body". Suppose that, in the example given above, you now want to re-freeze the cold water and re-vaporize the hot water by reversing the heat flow. In order to remove heat from a cold object and reject it to a hot one, one uses a refrigerator. A theoretically ideal refrigeration cycle will require the addition of 827 kJ of energy from an external source, and a total of 3084 kJ will be rejected to the hot water. The change in total entropy would then be -2257/273.15 + 3084/373.15 = 0.00191 kJ/K, and the effect was to cause heat to flow to a hot body from both a cold one and a hotter one. The process fully complies with the second Law.
It is vital to understand that the Second Law prohibits reductions in total entropy, that is, it forbids a negative generation of entropy; it does not forbid reductions in the intensive entropy of the individual bodies in the system nor does it require a positive generation of entropy. Notice again, in the refrigeration example above, that without the addition of 827 kJ from an outside source, the entropy generated during the process would have had a negative value, and it is this negative value that is disallowed by the Second Law.
Imagine a process in which heat flows from the cold water (causing it to freeze) into the hot water (causing it to boil). The entropy generation from that process would be -8.3 + 6.3 = -2.0 kJ/K, which would violate the Second Law, and in fact heat does not spontaneously flow from cold objects to hot ones.
There are several corollaries to the Second Law, one of which can be stated as follows: "In a closed system, total entropy increases for irreversible processes and remains constant for reversible processes". Irreversible processes are those that result in an increase in total entropy; such processes can only occur in one direction. For example, you can heat up a fluid by spinning a paddle in it, but you cannot apply the heat energy of a fluid to a paddle and make the paddle spin. You can heat two objects up by rubbing them together, but you cannot make two objects rub together by heating them up. Energy expended in irreversible processes is no longer available to do work, so it is referred to as being irreversibly lost.
Not all processes are irreversible. When you use a rotating shaft to raise a weight, you can harness all of the potential energy of the raised weight to make the shaft spin again. There is, therefore, no change in total entropy due to the work done in raising the weight. When you slowly pressurize a gas by moving a piston against it, you can recover all of the work done by allowing the piston to move back to its original position under the pressure of the gas. There is no change in total entropy when a gas is pressurized slowly, thus the process is completely reversible.
The entropy generation of a process is a measure of both the irreversibility and the efficiency of the process. If one compares two processes that perform the same amount of work, the process that generates the least total entropy is the least irreversible (the most reversible) and the most efficient.
Another corollary to the Second Law is "there can be no machine whose only effect is to cause heat to flow from a cold body to a warm body". Suppose that, in the example given above, you now want to re-freeze the cold water and re-vaporize the hot water by reversing the heat flow. In order to remove heat from a cold object and reject it to a hot one, one uses a refrigerator. A theoretically ideal refrigeration cycle will require the addition of 827 kJ of energy from an external source, and a total of 3084 kJ will be rejected to the hot water. The change in total entropy would then be -2257/273.15 + 3084/373.15 = 0.00191 kJ/K, and the effect was to cause heat to flow to a hot body from both a cold one and a hotter one. The process fully complies with the second Law.
It is vital to understand that the Second Law prohibits reductions in total entropy, that is, it forbids a negative generation of entropy; it does not forbid reductions in the intensive entropy of the individual bodies in the system nor does it require a positive generation of entropy. Notice again, in the refrigeration example above, that without the addition of 827 kJ from an outside source, the entropy generated during the process would have had a negative value, and it is this negative value that is disallowed by the Second Law.
THERE IS NO SUCH THING AS A “LOCAL VIOLATION” OF THE SECOND LAW
It has been erroneously proposed that there can be “local” violations of the Second Law, such as when a refrigerator causes heat to flow from a cold body to a hot one. In my experience, all of these proposals fail because either the system boundaries are incorrectly drawn, or each step of the process is not correctly understood, or both.
Refrigerators transfer heat from a low temperature body to a higher temperature body by means of the addition and rejection of an additional amount of heat. It is not possible to separate out this heat addition from an analysis of the cycle, and at no time during the cycle is there a violation of the 2nd Law.
Within the refrigeration cycle there are four phases:
You can see that the intensive entropy of any individual element of refrigerant cycles from high to low levels over the cycle; this in no way involves any violation of the Second Law.
You can see that during the cycle heat never flows from a hot object to a cold object. The heat rejected to the room is equal to that absorbed from the refrigerated space plus that added during the compression phase. The cycle fully complies with the statement "there can be no machine whose only effect is to cause heat to flow from a cold body to a warm body", because it also has the effect of causing heat to flow from a hot body to the warm body. Note also that this is intrinsic to the cycle itself, and is the case even if the source of the added heat is perfectly efficient.
Refrigerators transfer heat from a low temperature body to a higher temperature body by means of the addition and rejection of an additional amount of heat. It is not possible to separate out this heat addition from an analysis of the cycle, and at no time during the cycle is there a violation of the 2nd Law.
Within the refrigeration cycle there are four phases:
1. Compression, in which the enthalpy of the working fluid is increased at constant entropy, by the addition of energy. At the end of this phase the fluid is hotter than the air in the room.
2. Heat rejection (to the room) at a constant pressure, during which the enthalpy and entropy of the fluid are both decreased.
3. Expansion, in which the enthalpy of the working fluid is decreased at constant entropy. At the end of this phase the fluid is colder than the air in the refrigerated space, and is at a lower entropy than at the start of the compression phase.
4. Heat absorption (from the refrigerated space) at a constant pressure, during which the entropy and enthalpy of the fluid are increased to the same values they had at the start of the compression phase.
2. Heat rejection (to the room) at a constant pressure, during which the enthalpy and entropy of the fluid are both decreased.
3. Expansion, in which the enthalpy of the working fluid is decreased at constant entropy. At the end of this phase the fluid is colder than the air in the refrigerated space, and is at a lower entropy than at the start of the compression phase.
4. Heat absorption (from the refrigerated space) at a constant pressure, during which the entropy and enthalpy of the fluid are increased to the same values they had at the start of the compression phase.
You can see that the intensive entropy of any individual element of refrigerant cycles from high to low levels over the cycle; this in no way involves any violation of the Second Law.
You can see that during the cycle heat never flows from a hot object to a cold object. The heat rejected to the room is equal to that absorbed from the refrigerated space plus that added during the compression phase. The cycle fully complies with the statement "there can be no machine whose only effect is to cause heat to flow from a cold body to a warm body", because it also has the effect of causing heat to flow from a hot body to the warm body. Note also that this is intrinsic to the cycle itself, and is the case even if the source of the added heat is perfectly efficient.
(continued)
(EDITED 15MAR06 to correct a boneheaded math error, and to refine the explanation)
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