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The '''Second Law of Thermodynamics''' is the tendency towards disorder in the absence of intelligent intervention.  Heat never flows from a cold body to a warmer one, unless forced to do so by a man-made machine.  As the [[atheist]] scientist [[Isaac Asimov]] admitted:

The '''Second Law of Thermodynamics''' is the tendency toward disorder in the absence of intelligent intervention.  Heat never flows from a cold body to a warmer one, unless forced to do so by a man-made machine.  As the [[atheist]] scientist [[Isaac Asimov]] admitted:

{{Cquote|Another way of stating the second law then is: '''''The universe is constantly getting more disorderly'''''.  Viewed that way, we can see the second law all about us. We have to work to straighten a room, but left to itself it becomes a mess again very quickly and very easily. Even if we never enter it, it becomes dusty and musty. How difficult to maintain houses, and machinery, and our bodies in perfect working order: how easy to let them deteriorate. In fact, all we have to do is nothing, and '''''everything deteriorates, collapses, breaks down, wears out, all by itself -- and that is what the second law is all about'''''.|||Isaac Asimov, Smithsonian Institute Journal, June 1970, p. 6, emphasis added}}

{{Cquote|Another way of stating the second law then is: '''''The universe is constantly getting more disorderly'''''.  Viewed that way, we can see the second law all about us. We have to work to straighten a room, but left to itself it becomes a mess again very quickly and very easily. Even if we never enter it, it becomes dusty and musty. How difficult to maintain houses, and machinery, and our bodies in perfect working order: how easy to let them deteriorate. In fact, all we have to do is nothing, and '''''everything deteriorates, collapses, breaks down, wears out, all by itself -- and that is what the second law is all about'''''.|||Isaac Asimov, Smithsonian Institute Journal, June 1970, p. 6, emphasis added}}

The Second Law of Thermodynamics reflects the intrinsic uncertainty in nature, manifest in [[quantum mechanics]], which is overcome only by intelligent intervention.  [[Epistle to the Hebrews (Translated)#1:10-11|Hebrews 1:10]] states the universe shall "wear out" like a "garment", ''i.e.'', [[entropy]] is always increasing.

The Second Law of Thermodynamics reflects the intrinsic uncertainty in nature, manifest in [[quantum mechanics]], which is overcome only by intelligent intervention.  [[Epistle to the Hebrews (Translated)#1:10-11|Hebrews 1:10]] states the universe shall "wear out" like a "garment", ''i.e.'', [[entropy]] is always increasing.

This law makes it impossible to build a [[perpetual motion machine]] - the increase in entropy inevitably derails the system even if energy remains constant.  This law predicts that cables, cords, and wires, to self-entangle and require straightening.

This law makes it impossible to build a [[perpetual motion machine]] - the increase in entropy inevitably derails the system even if energy remains constant.  This law predicts that cables, cords, and wires, self-entangle and require straightening.

The Second Law of Thermodynamics disproves the [[atheistic]] [[Theory of Evolution]] and [[Theory of Relativity]], both of which deny a fundamental uncertainty to the physical world that leads to increasing disorder.

The Second Law of Thermodynamics disproves the [[atheistic]] [[Theory of Evolution]] and [[Theory of Relativity]], both of which deny a fundamental uncertainty to the physical world that leads to increasing disorder.

In the terminology of physics, the Second Law states that the [[entropy]] of an isolated or [[closed system]] never decreases.<ref>Much of this article could be considered to be a continuation of the [[thermodynamics]] article, which see.  That article provides some historical background, along with an explanation of the relationship between the Second Law and the increase in entropy.</ref>

In the terminology of physics, the Second Law states that the [[entropy]] of an isolated or [[closed system]] never decreases.<ref>Much of this article could be considered to be a continuation of the [[thermodynamics]] article.  That article provides some historical background, along with an explanation of the relationship between the Second Law and the increase in entropy.</ref>

==Entropy and disorder ==

==Entropy and disorder ==

In this context "increasing disorder" means the decline in organization that occurs without intelligent intervention.  Imagine your old room at your parent's house.  Remember how easy it was to let the room turn into a uniform mess (disorder) and remember how hard it was to clean it up until it fit a specific, non-uniform design (order).  Not cleaning up would always result in an increase of entropy in your room!

In this context "increasing disorder" means the decline in organization that occurs without intelligent intervention.  Imagine your old room at your parent's house.  Remember how easy it was to let the room turn into a uniform mess (disorder) and remember how hard it was to clean it up until it fit a specific, non-uniform design (order).  Not cleaning up would always result in an increase in entropy in your room!

The flow of energy (by heat exchange) to places with lower concentrations is called the "heat flow."

The flow of energy (by heat exchange) to places with lower concentrations is called the "heat flow."

The often-heard argument that this law disproves an eternal universe is true, because in that case maximum entropy would have been reached already. A counterargument to this would be to suggest that the universe is still in the process of approaching maximum entropy.

The often-heard argument is that this law disproves a universe that has existed forever, because in that case maximum entropy would have been reached already. A counterargument to this would be to suggest that the universe is eternal into the future and is still in the process of approaching maximum entropy.

There are many different ways of stating the Second Law of thermodynamics. An alternative statement of the law is that heat will tend not to flow from a cold body to a warmer one without intelligent intervention, or work, being done, as in the case of a [[refrigerator]].  Other statements include that it is impossible for an [[engine]] to convert [[heat]] perfectly (I.e. at 100% efficiency) into [[work]]. These statements are qualitative and stating the Second Law in terms of [[entropy]] makes the law quantitative.

There are many different ways of stating the Second Law of thermodynamics. An alternative statement of the law is that heat will tend not to flow from a cold body to a warmer one without intelligent intervention, or work, being done, as in the case of a [[refrigerator]].  Other statements include that it is impossible for an [[engine]] to convert [[heat]] perfectly (I.e. at 100% efficiency) into [[work]]. These statements are qualitative and stating the Second Law in terms of [[entropy]] makes the law quantitative.

where <math>\frac{dS_{universe}}{dt}</math> is the rate of change of [[entropy]] of the [[universe]] with respect to time.

where <math>\frac{dS_{universe}}{dt}</math> is the rate of change of [[entropy]] of the [[universe]] with respect to time.

Another way of viewing the Second Law is in terms of probability.  In nature there is no one to clean up the universe, only chances.  The chance of something becoming orderly is essentially zero, which it is a certainty that things will become more disorderly.

Another way of viewing the Second Law is in terms of probability.  In nature, there is no one to clean up the universe, only chances.  The chance of something becoming orderly is essentially zero, and it is a certainty that things will become more disorderly.

On a universal scale a tidy room would be a universe which has pockets of above average concentrations of energy (if you - incorrectly - assume relativity [[E=mc²]] this includes matter as well.)

On a universal scale a tidy room would be a universe that has pockets of above-average concentrations of energy (if you - incorrectly - assume relativity [[E=mc²]] this includes matter as well.)

==Second Law compared with other physical laws==

==Second Law compared with other physical laws==

Thermodynamics occupies an unusual place in the world of science, particularly at the high school and undergraduate levels.  The Second Law is the one that is especially peculiar.  (In fact, the other laws are comparatively mundane.  The first law is just a statement that heat is a form of energy, and that energy, whether in the form of heat or not, is conserved.  This was a very nontrivial result at first, but, with the understanding of heat and temperature that later developed, it's quite unremarkable.  The third law is a statement that absolute zero can't be reached by any finite number of Carnot cycles.<ref>[https://en.wikiversity.org/wiki/Carnot_engine Carnot Engine]</ref>  While true, its significance pales in comparison to that of the Second Law.)

Thermodynamics occupies an unusual place in the world of science, particularly at the high school and undergraduate levels.  The Second Law is an especially peculiar one.  (In fact, the other laws are comparatively mundane.  The first law is just a statement that heat is a form of energy, and that energy, whether in the form of heat or not, is conserved.  This was a nontrivial result at first, but, with the understanding of heat and temperature that later developed, it's quite unremarkable.  The third law is a statement that absolute zero can't be reached by any finite number of [[Carnot]] cycles.<ref>[https://en.wikiversity.org/wiki/Carnot_engine Carnot Engine]</ref>  While true, its significance pales in comparison to that of the Second Law.)

Perhaps what makes the Second Law so remarkable is that it describes ''irreversible'' phenomena.  In particular, it describes the observed fact that heat energy, in bodies that are not being externally manipulated by compression, etc., flows only from a warmer body to a cooler one.  When a warmer body is placed in contact with a cooler one, heat energy will flow (always preserving total energy, of course) from the warmer one to the cooler one.  The warmer one will cool off as it releases its energy, and the cooler one will warm up.  This process will continue until the two bodies reach the same temperature, or "thermal equilibrium".

Perhaps what makes the Second Law so remarkable is that it describes ''irreversible'' phenomena.  In particular, it describes the observed fact that heat energy, in bodies that are not being externally manipulated by compression, etc., flows only from a warmer body to a cooler one.  When a warmer body is placed in contact with a cooler one, heat energy will flow (always preserving total energy, of course) from the warmer one to the cooler one.  The warmer one will cool off as it releases its energy, and the cooler one will warm up.  This process will continue until the two bodies reach the same temperature, or "thermal equilibrium".

Until the development of [[statistical mechanics]], no one knew why this was so, or what temperature actually meant.  What was known was simply that a body with a higher temperature would send heat to a body with a lower temperature, no matter what the bodies were made of.

Until the development of [[statistical mechanics]], no one knew why this was so, or what temperature actually meant.  What was known was simply that a body with a higher temperature would send heat to a body with a lower temperature, no matter what the bodies were made of.

The fact that this kind of heat flow is irreversible makes the whole field of thermodyamics lie outside of the realm of classical Newtonian mechanics or Relativistic mechanics.  In Newtonian or Relativistic mechanics, every phenomenon can go in reverse order.  The catchy phrase [[Arrow of time]] (or "time's arrow") was coined by [[Arthur Eddington]] to denote this one-way behavior not shared by other theories of physics.<ref>''The Nature of the Physical World'', Arthur Eddington, MacMillan, 1929, ISBN 0-8414-3885-4</ref>

The fact that this kind of heat flow is irreversible makes the whole field of thermodynamics lie outside of the realm of classical Newtonian mechanics or Relativistic mechanics.  In Newtonian or Relativistic mechanics, every phenomenon can go in reverse order.  The catchy phrase [[Arrow of time]] (or "time's arrow") was coined by [[Arthur Eddington]] to denote this one-way behavior not shared by other theories of physics.<ref>''The Nature of the Physical World'', Arthur Eddington, MacMillan, 1929, ISBN 0-8414-3885-4</ref>

The field of statistical mechanics attributes the increase in entropy to the statistical tendencies of huge aggregates of particles at the molecular or atomic level.  While Newtonian and Relativistic mechanics can, in principle, precisely describe assemblages of any number of particles, in practice they are not directly applied to the behavior of bulk material.  That is, they are not applied to a number of particles on the order of Avogadro's number.

The field of statistical mechanics attributes the increase in entropy to the statistical tendencies of huge aggregates of particles at the molecular or atomic level.  While Newtonian and Relativistic mechanics can, in principle, precisely describe assemblages of any number of particles, in practice they are not directly applied to the behavior of bulk material.  That is, they are not applied to a number of particles on the order of Avogadro's number.

Statistical mechanics makes no assumptions about the microscopic cause of the seemingly random behavior.  Statistical mechanics was developed in the 19^th century prior to quantum mechanics, and does not depend on the [[Heisenberg uncertainty principle]].  The quantum mechanical uncertainty goes away at the microscopic level once the system is observed and the wave function collapses.

Statistical mechanics makes no assumptions about the microscopic cause of the seemingly random behavior.  Statistical mechanics was developed in the 19^th century prior to [[quantum mechanics]], and does not depend on the [[Heisenberg uncertainty principle]].  The quantum mechanical uncertainty goes away at the microscopic level once the system is observed and the wave function collapses.

It needs to be emphasized that the peculiarities of thermodynamics, with the phenomenon fo irreversibility and the "arrow of time", ''in no way'' contradict the (reversible) processes of classical Galilean, Newtonian, Lagrangian, or Hamiltonian physics, or of special or general relativity.  Those formulations are precise in the regimes in which the behavior of individual particles are analyzed.  When two gas molecules collide in the [[Kinetic theory]], that collision is perfectly reversible.  It is only when one goes into a problem domain in which the bulk behavior of huge numbers (on the order of Avogadro's number) of particles are analyzed, without regard for the individual particles, that thermodynamics and statistical mechanics come into play.

It needs to be emphasized that the peculiarities of thermodynamics, with the phenomenon of irreversibility and the "arrow of time", ''in no way'' contradict the (reversible) processes of classical Galilean, Newtonian, Lagrangian, or Hamiltonian physics, or of special or general relativity.  Those formulations are precise in the regimes in which the behavior of individual particles is analyzed.  When two gas molecules collide in the [[Kinetic theory]], that collision is perfectly reversible.  It is only when one goes into a problem domain in which the bulk behavior of huge numbers (on the order of Avogadro's number) of particles are analyzed, without regard for the individual particles, that thermodynamics and statistical mechanics come into play.

==Elementary probability and statistics==

==Elementary probability and statistics==

If you flipped a coin 20 times and it came up heads each time, you would consider that to be a remarkable occurrence.  (Perhaps so much so that you would inspect the coin to be sure it didn't have heads on both sides.)  If you tried it and got tttthtththhhththhthh, you would probably not consider it remarkable.  Yet each of these outcomes is equally probable: about 1 in 10⁶.  If you shuffled a deck of cards and found them all in exact order from the 2 of clubs to the ace of spades, you would consider that to be very remarkable.  But if you got the distribution shown in the illustration on page 314 of Alfred Sheinwold's ''5 Weeks to Winning Bridge'', you would probably consider it just "random".  Yet each of these orderings has the same probability of occurring&mdash;1 in 52 factorial, which is about 10⁶⁶.<ref>Actually, we're ignoring the fact that bridge players sort their cards by suit, and the diagram shows the result of the sorting.</ref>

If you flipped a coin 20 times and it came up heads each time, you would consider that to be a remarkable occurrence.  (Perhaps so much so that you would inspect the coin to be sure it didn't have heads on both sides.)  If you tried it and got tttthtththhhththhthh, you would probably not consider it remarkable.  Yet each of these outcomes is equally probable: about 1 in 10⁶.  If you shuffled a deck of cards and found them all in exact order from the 2 of clubs to the ace of spades, you would consider that to be very remarkable.  But if you got the distribution shown in the illustration on page 314 of Alfred Sheinwold's ''5 Weeks to Winning Bridge'', you would probably consider it just "random".  Yet each of these orderings has the same probability of occurring&mdash;1 in 52 factorial, which is about 10⁶⁶.<ref>Actually, we're ignoring the fact that bridge players sort their cards by suit, and the diagram shows the result of the sorting.</ref>

For small sets such as coin tosses or card shufflings, what constitutes "random" vs. "well ordered" is in the eye of the beholder.  If a room in your house started in a state that most people would consider "neat and tidy", and you went into that room every day, picked up a random obect, and threw it against a random wall, after a month most people would consider the room a mess.  But, once again, this is hard to quantify.  The kinds of statistical analyses that are required for the study of thermodynamics have to be much more careful than this.  The kind of folksy quotations in popular articles about messy rooms, as in the Isaac Asimov quote, may sell magazines, but they don't shed much light on how thermodynamics works.

For small sets such as coin tosses or card shufflings, what constitutes "random" vs. "well ordered" is in the eye of the beholder.  If a room in your house started in a state that most people would consider "neat and tidy", and you went into that room every day, picked up a random object, and threw it against a random wall, after a month most people would consider the room a mess.  But, once again, this is hard to quantify.  The kinds of statistical analyses that are required for the study of thermodynamics have to be much more careful than this.  The kind of folksy quotations in popular articles about messy rooms, as in the Isaac Asimov quote, may sell magazines, but they don't shed much light on how thermodynamics works.

What is needed is an analysis of ''aggregate properties'', not individual items.  We need to quantify the results.  For the case of the coin toss, we might ask how many times we got heads.  The probabilities can be worked out; they are a "Gaussian distribution", also known as a "bell curve".  The probability of heads 0 times out of 20 is 1 in 1048576.  Getting heads exactly 1 time is .00002, and so on, as shown in this table.  Notice that getting heads exactly 10 times is the most probable outcome, but its probability is still only 18%.  If we did the experiment a larger number of times, the probability of exactly 50% heads would still be higher than any other, but it would be quite small.  What is important is the probability of getting a certain number of heads ''or less''.

What is needed is an analysis of ''aggregate properties'', not individual items.  We need to quantify the results.  For the case of the coin toss, we might ask how many times we got heads.  The probabilities can be worked out; they are a "Gaussian distribution", also known as a "bell curve".  The probability of heads 0 times out of 20 is 1 in 1048576.  Getting heads exactly 1 time is .00002, and so on, as shown in this table.  Notice that getting heads exactly 10 times is the most probable outcome, but its probability is still only 18%.  If we did the experiment a larger number of times, the probability of exactly 50% heads would still be higher than any other, but it would be quite small.  What is important is the probability of getting a certain number of heads ''or less''.

*You can't ask any questions about individual items&mdash;air molecules don't have labels like "Jack of Diamonds".  You can only ask questions about the aggregate behavior of macroscopic pieces of space.

*You can't ask any questions about individual items&mdash;air molecules don't have labels like "Jack of Diamonds".  You can only ask questions about the aggregate behavior of macroscopic pieces of space.

*While the probabilities of certain outcomes can be mathematically calculated, they are so small that, as a practical matter, we can say that '''they do not occur'''.  People sometimes like to say things like "The Second Law of Thermodynamics means that it is very unlikely that heat will travel from a colder object to a warmer one."  That's a fallacious way of thinking about it.  It is a [[statistical impossibility]]&mdash;it just doesn't occur.

*While the probabilities of certain outcomes can be mathematically calculated, they are so small that, as a practical matter, we can say that '''they do not occur'''.  People sometimes like to say things like "The Second Law of Thermodynamics means that it is very unlikely that heat will travel from a colder object to a warmer one."  That's a fallacious way of thinking about it.  It is a [[statistical impossibility]]&mdash;it just doesn't occur.

*An example is the question of how likely it is that all the air molecules in a room will move to one corner, asphyxiating everyone.<ref>Actually, conservation of momentum requires that we consider half the molecules going to one corner and the other half to the opposite corner.</ref>  This is sometimes worked out in physics classes.  But the conclusion has to be that this occurrence, or anything remotely resembling it, might have a probability on the order of 1 in 10^10²³&mdash;it just doesn't happen.

*An example is the question of how likely it is that all the air molecules in a room will move to one corner, asphyxiating everyone.<ref>Actually, conservation of momentum requires that we consider half the molecules going to one corner and the other half to the opposite corner.</ref>  This is sometimes worked out in physics classes.  But the conclusion has to be that this occurrence, or anything remotely resembling it, might have a probability on the order of 1 in 10^10²³&mdash; it just doesn't happen.

==Aren't we cheating when we say that heat flows from a warmer body to a colder one, when all we really know is that it "probably" flows that way?==

==Aren't we cheating when we say that heat flows from a warmer body to a colder one, when all we really know is that it "probably" flows that way?==

Well, yes, and no.  The laws of probability and statistical mechanics are precisely true, since they are mathematical theorems.  They are as precise as that 2+2=4 exactly.  It's their application to the real world of molecules and such that is merely "probably" correct.    When we say that heat flows downward in macroscopic objects (ice cubes, teapots, Carnot engines<ref>[https://en.wikiversity.org/wiki/Carnot_engine Carnot Engine]</ref>), what we really mean is that it flows downward with a probability of 99.999<put in Avogadro's number of 9's here>999 percent.

Well, yes, and no.  The laws of probability and statistical mechanics are precisely true, since they are mathematical theorems.  They are as precise as that 2+2=4 exactly.  It's their application to the real world of molecules and such that is merely "probably" correct.    When we say that heat flows downward in macroscopic objects (ice cubes, teapots, Carnot engines<ref>[https://en.wikiversity.org/wiki/Carnot_engine Carnot Engine]</ref>), what we really mean is that it flows downward with a probability of 99.999<put in Avogadro's number of 9's here>999 percent.

Everyone, scientists and lay people alike, accept this as true.  It is the basis for just about everything, including breathing.  No one ever questions the reading on the pressure gauge of a gas canister on the grounds that it is only probably correct, or is surprised when one blows into a balloon and it expands.

Everyone, scientists and laypeople alike, accept this as true.  It is the basis for just about everything, including breathing.  No one ever questions the reading on the pressure gauge of a gas canister because it is only probably correct, or is surprised when one blows into a balloon and it expands.

So the fine philosophical point about it being only probably correct is just that&mdash;a fine philosophical point.

So the fine philosophical point about it being only probably correct is just that&mdash;a fine philosophical point.

==Application to molecular behavior==

==Application to molecular behavior==

[[Statistical mechanics]] is the application of probability to enormous numbers like this.  It was developed, along with the [[kinetic theory]], by [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Rudolf Clausius]], [[Benoît Paul Émile Clapeyron]], and others, during the 19^th century.  The development of the kinetic theory of gases, statistical mechanics, and thermodynamics revolutionized 19^th century physics.  It was recognized that, while we can't analyze the behavior of every molecule, we can analyze the statistical behavior of macroscopic assemblages.  When gas molecules collide, they can transfer energy in a manner that leads to the principle of ''equipartition of energy''.  This, plus the constraints on conservation of the total energy, leads to the ''Maxwell-Boltzmann'' distribution of molecular energies.  From this, one can deduce the properties of volume, pressure, and temperature, leading to Boyle's law and Charles' law, among others.  Temperature was found to be just the average energy per molecule.  (Actually, the average energy per "degree of freedom".)   

[[Statistical mechanics]] is the application of probability to enormous numbers like this.  It was developed, along with the [[kinetic theory]], by [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Rudolf Clausius]], [[Benoît Paul Émile Clapeyron]], and others, during the 19^th century.  The development of the kinetic theory of gases, statistical mechanics, and thermodynamics revolutionized 19^th century physics.  It was recognized that, while we can't analyze the behavior of every molecule, we can analyze the statistical behavior of macroscopic assemblages.  When gas molecules collide, they can transfer energy in a manner that leads to the principle of ''equipartition of energy''.  This, plus the constraints on the conservation of the total energy, leads to the ''Maxwell-Boltzmann'' distribution of molecular energies.  From this, one can deduce the properties of volume, pressure, and temperature, leading to Boyle's law and Charles' law, among others.  Temperature was found to be just the average energy per molecule.  (Actually, the average energy per "degree of freedom".)   

The fact that heat only flows downhill, and that entropy never decreases, is now just a consequence of the "most probable distribution" principle, or equipartition principle, from mathematical statistics, albeit at a vastly larger scale.

The fact that heat only flows downhill, and that entropy never decreases, is now just a consequence of the "most probable distribution" principle, or equipartition principle, from mathematical statistics, albeit at a vastly larger scale.

Note that the Boltzmann constant has taken a value of 1 to simplify the maths.

Note that the Boltzmann constant has taken a value of 1 to simplify the maths.

So the state that we would expect to find the system in, the last one, has the highest entropy. However, the system could be in this state (10 in left, 10 in the right) and, just by chance, all the molecules could make their way to the left hand side of the box. This corresponds to a '''decrease''' of entropy. This example could be expanded up to a room, so why do we never see all the air in a room suddenly move to one end? The reason is that it is so unlikely, perhaps less than <math>10^{-10^{26}}</math>, that it essentially never occurs.<ref>{{cite book

So the state that we would expect to find the system in, the last one, has the highest entropy. However, the system could be in this state (10 in left, 10 in the right) and, just by chance, all the molecules could make their way to the left-hand side of the box. This corresponds to a '''decrease''' of entropy. This example could be expanded up to a room, so why do we never see all the air in a room suddenly move to one end? The reason is that it is so unlikely, perhaps less than <math>10^{-10^{26}}</math>, that it essentially never occurs.<ref>{{cite book

|author=Hugh D. Young and Roger A. Freedman

|author=Hugh D. Young and Roger A. Freedman

|title=University Physics with Modern Physics

|title=University Physics with Modern Physics

|pages=

|pages=

|quote=

|quote=

|language=English}}</ref> Hence it may be '''assumed''' that for most systems entropy '''never''' decreases. This is known as the [[fluctuation theorem]].

|language=English}}</ref> Hence it may be '''assumed''' that for most systems entropy '''never''' decreases. This is known as the [[fluctuation theorem]].

==Thermodynamic definition of entropy==

==Thermodynamic definition of entropy==

::<math>dS = \frac{dQ}{dt}</math>&nbsp;&nbsp;&nbsp;&nbsp;'''S''' = entropy, '''Q''' = heat energy, '''T''' = temperature

::<math>dS = \frac{dQ}{dt}</math>&nbsp;&nbsp;&nbsp;&nbsp;'''S''' = entropy, '''Q''' = heat energy, '''T''' = temperature

The definition as a differential implies that it can be considered to be independent up to an additive constant.  This is true; for problems in thermodynamics it doesn't matter whether a constant is added to the entropy everywhere.  (But this is not true for the definitions used in combinatorics and mathematical statistics.)

The definition of a differential implies that it can be considered to be independent up to an additive constant.  This is true; for problems in thermodynamics it doesn't matter whether a constant is added to the entropy everywhere.  (But this is not true for the definitions used in combinatorics and mathematical statistics.)

The definition as a differential could mislead one into thinking that integration around some closed path could lead to a different value, that is, that '''dS''' is not an ''exact form''.  This is not correct&mdash;'''dS''' is an exact form, and entropy is a true state variable.  A mole of uniform Nitrogen at [[standard temperature and pressure]] (STP) always has the same entropy, once one chooses the additive constant for the system.  (It is <math>29.1\ \log T\ \frac{Joules}{Kelvin}</math>; see below.)  A mole of nitrogen that is partly at one temperature and partly at another will have a lower entropy; the entropy will increase as the gas fractions mix.

The definition as a differential could mislead one into thinking that integration around some closed path could lead to a different value, that is, that '''dS''' is not an ''exact form''.  This is not correct&mdash;'''dS''' is an exact form, and entropy is a true state variable.  A mole of uniform Nitrogen at [[standard temperature and pressure]] (STP) always has the same entropy, once one chooses the additive constant for the system.  (It is <math>29.1\ \log T\ \frac{Joules}{Kelvin}</math>; see below.)  A mole of nitrogen that is partly at one temperature and partly at another will have a lower entropy; the entropy will increase as the gas fractions mix.

The measure of entropy of a specific thing is in Joules per Kelvin, as can be seen from the definition as '''dQ'''/'''T'''.  Entropy is an "extensive" quantity' like energy or momentum&mdash;two teapots have twice the entropy of one teapot.  So the entropy of some kind of substance (e.g.&nbsp;nitrogen at STP) could be measured in Joules per (mole Kelvin).  This happens to be the same dimensions as the ''universal gas constant'' '''R'''.

The measure of the entropy of a specific thing is in Joules per Kelvin, as can be seen from the definition as '''dQ'''/'''T'''.  Entropy is an "extensive" quantity' like energy or momentum&mdash;two teapots have twice the entropy of one teapot.  So the entropy of some kind of substance (e.g.&nbsp;nitrogen at STP) could be measured in Joules per (mole Kelvin).  This happens to be the same dimensions as the ''universal gas constant'' '''R'''.

==Entropy in popular culture&mdash;intuitive notions of entropy and "randomness"==

==Entropy in popular culture&mdash;intuitive notions of entropy and "randomness"==

==Reversibility and irreversibility==

==Reversibility and irreversibility==

[[Reversible process|Reversibility]] is a theoretical concept related to the Second Law of Thermodynamics. A process is reversible if the net heat and work exchange between the system and the surroundings is zero for the process running forwards and in reverse. This means the process does not generate entropy. In reality, no process is completely reversible. Irreversibility is a quantity sometimes called "lost work" and is equal to the difference between a process' actual work and reversible work. Irreversibility is also equal to a process' entropy generation multiplied by a reference temperature.

[[Reversible process|Reversibility]] is a theoretical concept related to the Second Law of Thermodynamics. A process is reversible if the net heat and work exchange between the system and the surroundings is zero for the process running forward and in reverse. This means the process does not generate entropy. In reality, no process is completely reversible. Irreversibility is a quantity sometimes called "lost work" and is equal to the difference between a process' actual work and reversible work. Irreversibility is also equal to a process' entropy generation multiplied by a reference temperature.

==Trend toward uniformity in the universe==

==Trend toward uniformity in the universe==

The universe will always become increasingly uniform, that is: heat will spread until the entire [[universe]] has the [[temperature]] and energy level (in an [[isolated system]] heat will always spread from a place where there is a lot of heat to a place where there is less until balance is achieved), forces will continue to work until a universal balance has been achieved.

The universe will always become increasingly uniform, that is: heat will spread until the entire [[universe]] has the [[temperature]] and energy level (in an [[isolated system]] heat will always spread from a place where there is a lot of heat to a place where there is less until balance is achieved), forces will continue to work until a universal balance has been achieved.

In this final state the universe is one uniform space where nothing happens and no work (moving something) can be done since there are no above average concentrations of energy left.

In this final state the universe is one uniform space where nothing happens and no work (moving something) can be done since there are no above-average concentrations of energy left.

This state is called maximum entropy and is said to be in perfect disorder (although intuitively its uniformity would seem to be a state of perfect order) because it has become impossible to determine what happened in the past.  ''i.e.'' There are an infinite number of ways (histories of the universe) maximum entropy could have been reached.

This state is called maximum entropy and is said to be in perfect disorder (although intuitively its uniformity would seem to be a state of perfect order) because it has become impossible to determine what happened in the past.  ''i.e.'' There are an infinite number of ways (histories of the universe) maximum entropy could have been reached.

==The types of systems governed by the Law==

==The types of systems governed by the Law==

The Second Law of Thermodynamics is essentially a conservation law, like conservation of energy, or momentum, or mass.  As such, it only applies to isolated systems.  One would not perform an experiment to show conservation of energy in a swinging clock pendulum if one pushes on the pendulum, and one can't show conservation of momentum of a baseball at the instant that it is hit by a bat.  By the same token, the Second Law can't be trusted when applied to a system that heat energy is entering or leaving.  Adding or removing matter would be an even more serious failure.

The Second Law of Thermodynamics is essentially a conservation law, like conservation of energy, or momentum, or mass.  As such, it only applies to isolated systems.  One would not perform an experiment to show the conservation of energy in a swinging clock pendulum if one pushes on the pendulum, and one can't show the conservation of momentum of a baseball at the instant that it is hit by a bat.  By the same token, the Second Law can't be trusted when applied to a system which heat energy is entering or leaving.  Adding or removing matter would be an even more serious failure.

There is only one type of system that the Second Law of Thermodynamics applies to: an [[isolated system]]. An isolated system is one that does not exchange matter or energy with its surroundings.

There is only one type of system that the Second Law of Thermodynamics applies to: an [[isolated system]]. An isolated system is one that does not exchange matter or energy with its surroundings.

Hence the Second Law of Thermodynamics does not strictly apply to the following types of system:

Hence the Second Law of Thermodynamics does not strictly apply to the following types of systems:

* [[Closed system]] - Exchanges energy, but not matter, with its surroundings

* [[Closed system]] - Exchanges energy, but not matter, with its surroundings

* Open system - Exchanges both matter and energy with its surroundings

* Open system - Exchanges both matter and energy with its surroundings

{{cquote|The second law of thermodynamics, or the law of increased entropy, says that over time, everything breaks down and tends towards disorder - entropy!  Entropy is the amount of UNusable energy in any systems; that system could be the earth's environment or the universe itself.  The more entropy there is, the more disorganisation and chaos.   

{{cquote|The second law of thermodynamics, or the law of increased entropy, says that over time, everything breaks down and tends towards disorder - entropy!  Entropy is the amount of UNusable energy in any systems; that system could be the earth's environment or the universe itself.  The more entropy there is, the more disorganisation and chaos.   

Therefore, if no outside force is adding energy to an isolated system to help renew it, it will eventually burn out (heat death).  This can be applied to a sun as well as a cup of tea - left to themselves, both will grow cold.  You can heat up a cold tea, you cannot heat up a cold sun.  NOTE: when a hot tea in an air tight room goes cold (loses all it's energy) not only do we NOT expect the process to reverse by natural causes (ie. the tea will get hot again), but both room temp and tea temp will be equal.  Keep that in mind as you read the next paragraph.

Therefore, if no outside force is adding energy to an isolated system to help renew it, it will eventually burn out (heat death).  This can be applied to a sun as well as a cup of tea - left to themselves, both will grow cold.  You can heat up a cold tea, you cannot heat up a cold sun.  NOTE: when a hot tea in an air-tight room goes cold (loses all its energy) not only do we NOT expect the process to reverse by natural causes (ie. the tea will get hot again), but both room temp and tea temp will be equal.  Keep that in mind as you read the next paragraph.

Look at it like this, because the energy in the universe is finite and no new energy is being added to it (1st law), and because the energy is being used up (2nd law), the universe cannot be infinite.  If our universe was infinite but was using up a finite supply of energy, it would have suffered 'heat death' a long time ago!  If the universe was infinite all radioactive atoms would have decayed and the universe would be the same temperature with no hot spots, no bright burning stars.  Since this is not true, the universe must have begun a finite time ago.<ref>[http://www.whybelieveingod.net/istheuniverseinfinite.htm Is the Universe Infinite?  Past beliefs and implications], Why believe in God? website</ref>}}  

Look at it like this, because the energy in the universe is finite and no new energy is being added to it (1st law), and because the energy is being used up (2nd law), the universe cannot be infinite.  If our universe was infinite but was using up a finite supply of energy, it would have suffered 'heat death' a long time ago!  If the universe was infinite all radioactive atoms would have decayed and the universe would be the same temperature with no hot spots, no bright burning stars.  Since this is not true, the universe must have begun a finite time ago.<ref>[http://www.whybelieveingod.net/istheuniverseinfinite.htm Is the Universe Infinite?  Past beliefs and implications], Why believe in God? website</ref>}}  

Thus, the First Law of Thermodynamics and the Second Law of Thermodynamics suggests that the [[universe]] had a beginning.<ref>

Thus, the First Law of Thermodynamics and the Second Law of Thermodynamics suggests that the [[universe]] had a beginning.<ref>

*[http://www.creationencounter.com/space/lawsofscience.php CAN LAWS OF SCIENCE EXPLAIN THE ORIGIN OF THE UNIVERSE?]

*[http://www.creationencounter.com/space/lawsofscience.php CAN LAWS OF SCIENCE EXPLAIN THE ORIGIN OF THE UNIVERSE?]

*[http://cavern.uark.edu/~cdm/creation/universeorigin.htm Evidence for the Supernatural Creation of the Universe] by Patrick R. Briney, Ph.D.

*[http://cavern.uark.edu/~cdm/creation/universeorigin.htm Evidence for the Supernatural Creation of the Universe] by Patrick R. Briney, Ph.D.

*[https://creation.com/eternal-universe Has the universe always existed?]</ref> This argument is similar to the argument for the [[big bang]], that the universe is expanding now, so in the past it must have been smaller, and since there is a limit to how small the universe can be, it points to a beginning. In this argument, it is entropy that has a lower limit.

*[https://creation.com/eternal-universe Has the universe always existed?]</ref> This argument is similar to the argument for the [[big bang]], that the universe is expanding now, so in the past it must have been smaller, and since there is a limit to how small the universe can be, it points to a beginning. In this argument, it is entropy that has a lower limit.

However, the statistical nature of the second law mean that it is not firmly true. If the universe is infinite in time, then eventually all possibilities, no matter how small, are played out. In this way, the universe could reach maximum entropy and then happen, by chance, to return to a low entropy state. This would happen an infinite number of times. Hence we could be in the process of entropy increasing and the universe need nor have a beginning.

However, the statistical nature of the second law means that it is not firmly true. If the universe is infinite in time, then eventually all possibilities, no matter how small, are played out. In this way, the universe could reach maximum entropy and then happen, by chance, to return to a low entropy state. This would happen an infinite number of times. Hence we could be in the process of entropy increasing and the universe need nor have a beginning.

== The 1st and 2nd laws of thermodynamics, theism and the origins of the universe ==

== The 1st and 2nd laws of thermodynamics, theism and the origins of the universe ==