Changes

*''Chemical thermodynamics'', which is heat and energy transfers involving chemical reactions within chemical systems.

*''Chemical thermodynamics'', which is heat and energy transfers involving chemical reactions within chemical systems.

Thermodynamics has an emphasis on a beginning or initial state of a system, and an end or final state of a system, with the system being all of the interacting components on this energy path.  Measurements in thermodynamics are usually reported on the [[International System of Units#Kelvin|Kelvin scale]] <ref>David Halliday, "Fundamentals of Physics Extended", John Wiley & Sons, New York, 1997 </ref>

Thermodynamics has an emphasis on a beginning or initial state of a system, and an end or final state of a system, with the system being all of the interacting components on this energy path.  Measurements in thermodynamics are usually reported on the [[International System of Units#Kelvin|Kelvin scale]] <ref>David Halliday, "Fundamentals of Physics Extended", John Wiley & Sons, New York, 1997</ref>

==History==

==History==

The downfall of Lavoisier's caloric theory happened at the arsenal in Munich, Germany.  The Bavarian minister of war was a British expatriate, Sir Benjamin Thompson, and he observed that work was being converted into heat by observing the boring of a cannon.  If caloric theory was correct, he reasoned, no more heat would be made once all of the caloric was removed from the cannon at the atomic level, yet his observations on this procedure - including a cannon bored while under water - demonstrated that work can be converted into heat, like the steam engines of his time converting heat into work.   

The downfall of Lavoisier's caloric theory happened at the arsenal in Munich, Germany.  The Bavarian minister of war was a British expatriate, Sir Benjamin Thompson, and he observed that work was being converted into heat by observing the boring of a cannon.  If caloric theory was correct, he reasoned, no more heat would be made once all of the caloric was removed from the cannon at the atomic level, yet his observations on this procedure - including a cannon bored while under water - demonstrated that work can be converted into heat, like the steam engines of his time converting heat into work.   

James Joule in 1849 made a precise determination of the mechanical equivalent of heat into work.  His stirring of water in a pot (work input with a mechanical stirring rod, caused by the motion of a 1-kg weight falling 42.4 cm) caused a temperature increase (heat output); his homemade, yet very-precise thermometers recorded the conversion factor.  The unit of energy is now called the ''[[International_System_of_Units#Joule|joule]]''.  4.2 joules of energy can raise one gram of water 1 degree Celsius, an amount called one calorie.  (The large-C "Calorie" used in nutritional measure is 1000 small-c calories.)

James Joule in 1849 made a precise determination of the mechanical equivalent of heat into work.  His stirring of water in a pot (work input with a mechanical stirring rod, caused by the motion of a 1-kg weight falling 42.4&nbsp;cm) caused a temperature increase (heat output); his homemade, yet very-precise thermometers recorded the conversion factor.  The unit of energy is now called the ''[[International System of Units#Joule|joule]]''.  4.2 joules of energy can raise one gram of water 1 degree Celsius, an amount called one calorie.  (The large-C "Calorie" used in nutritional measure is 1000 small-c calories.)

 

 

==[[First Law of Thermodynamics]]==

==[[First Law of Thermodynamics]]==

Joule, and others, continued in other experiments, noting the pressure changes caused by electrically-heated gases, and achieved similar results.  This in turn led to a number of other scientists to research in this area, among them the German physicists Rudolf Clausius and Hermann von Helmholtz in the 1840's.  This led to the general acceptance of [[Conservation of Energy]] as a clear and precise principle.  Clausius stated in 1850:

Joule, and others, continued in other experiments, noting the pressure changes caused by electrically-heated gases, and achieved similar results.  This in turn led to a number of other scientists to research in this area, among them the German physicists Rudolf Clausius and Hermann von Helmholtz in the 1840's.  This led to the general acceptance of [[Conservation of Energy]] as a clear and precise principle.  Clausius stated in 1850:

:''"In any process, energy can be changed from one form to another, but it is never created or destroyed."''

:''"In any process, energy can be changed from one form to another, but it is never created or destroyed."''

This principle notably included heat as a form of energy, which was the first law of thermodynamics.  Hot objects contain potential energy in the form of their heat, and all the usual rules of transformation between potential and kinetic energy apply.  When an electric current is passed through a resistor, the electrical energy is converted to heat energy, and the resistor gets hotter.  Everything seemed to work out accurately.

This principle notably included heat as a form of energy, which was the first law of thermodynamics.  Hot objects contain potential energy in the form of their heat, and all the usual rules of transformation between potential and kinetic energy apply.  When an electric current is passed through a resistor, the electrical energy is converted to heat energy, and the resistor gets hotter.  Everything seemed to work out accurately.

Of course, in all experiments that attempt to tally energy (or other properties) accurately, one must be careful to avoid outside interference.  Newton's formula <math>F = ma\,</math> requires that no unaccounted-for forces are acting on the object.  Similarly, in thermodynamics, one must take into account any possible sources of heat into or out of the entity under test.  This is often described by saying that the law of thermodynamics apply only to "isolated", or "closed", systems.  If a system can interact with some external entity, that entity's properties must be taken into account.

Of course, in all experiments that attempt to tally energy (or other properties) accurately, one must be careful to avoid outside interference.  Newton's formula <math>F = ma\,</math> requires that no unaccounted-for forces are acting on the object.  Similarly, in thermodynamics, one must take into account any possible sources of heat into or out of the entity under test.  This is often described by saying that the law of thermodynamics apply only to "isolated", or "closed", systems.  If a system can interact with some external entity, that entity's properties must be taken into account.

Scientists had mostly figured out a linear relationship between temperature rise and change in heat energy.  This is called the ''specific heat'', in joules per degree of temperature rise per gram of substance.  For example, the specific heat of water is 4.2 joules per gram per degree of temperature rise.

Scientists had mostly figured out a linear relationship between temperature rise and change in heat energy.  This is called the ''specific heat'', in joules per degree of temperature rise per gram of substance.  For example, the specific heat of water is 4.2 joules per gram per degree Celsius of temperature rise.

Heat engines (that is, steam engines) were being used on an industrial scale by then, but scientists still didn't know what temperature really meant.  And they didn't know why it only flows "downhill".  Also, while other forms of energy (as in running electricity through a resistor) could be converted to heat with essentially perfect efficiency, converting the other way (as in a steam engine) was very inefficient.  No one knew why.

Heat engines (that is, steam engines) were being used on an industrial scale by then, but scientists still didn't know what temperature really meant.  And they didn't know why it only flows "downhill".  Also, while other forms of energy (as in running electricity through a resistor) could be converted to heat with essentially perfect efficiency, converting the other way (as in a steam engine) was very inefficient.  No one knew why.

The clues that unraveled this mystery came from the study of gases, which had been going on for some time before.  [[Boyle's Law]], formulated in the 1660's, stated that, for a given sample of gas at a fixed temperature, the pressure was inversely proportional to the volume.  That is,

The clues that unravelled this mystery came from the study of gases, which had been going on for some time before.  [[Boyle's Law]], formulated in the 1660's, stated that, for a given sample of gas at a fixed temperature, the pressure was inversely proportional to the volume.  That is,

:<math>PV = constant</math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;where the constant depends on the amount and type of the gas sample

:<math>PV = constant</math>

[[Charles' Law]], formulated in the 1780's, stated that, for a given sample of gas at a fixed pressure, the volume was directly proportional the the "absolute" temperature.  That is,

 

:<math>V/T = constant</math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;where the constant depends on the amount and type of the gas sample

where the constant depends on the amount and type of the gas sample.

 

[[Charles' Law]], formulated in the 1780s, stated that, for a given sample of gas at a fixed pressure, the volume was directly proportional the "absolute" temperature.  That is,

:<math>V/T = constant</math>

 

where the constant depends on the amount and type of the gas sample

This required that the temperature scale be modified.  The necessary scale was known as absolute temperature, now known as [[International System of Units#Kelvin|Kelvin scale]].  All thermodynamic measurements are in Kelvins.

This required that the temperature scale be modified.  The necessary scale was known as absolute temperature, now known as [[International System of Units#Kelvin|Kelvin scale]].  All thermodynamic measurements are in Kelvins.

Where X is some constant that is characteristic of the gas sample.  It's easy to see that X is proportional to the amount of gas (2 grams of gas will have twice the volume of 1 gram).  So X is actually the amount of gas, measured in some convenient units (grams, moles, molecules), times some number that is characteristic of the gas.   

Where X is some constant that is characteristic of the gas sample.  It's easy to see that X is proportional to the amount of gas (2 grams of gas will have twice the volume of 1 gram).  So X is actually the amount of gas, measured in some convenient units (grams, moles, molecules), times some number that is characteristic of the gas.   

In the 1810's, Gay-Lussac and Avogadro made an amazing discovery:  The mysterious constant is just the molecular weight of the gas, if the amount of gas is measured in the right units.  The right unit to use is the ''mole'', which is the mass, in grams, that matches the molecular weight of the gas.  (By then atomic weights and molecular weights were beginning to be understood.)  So, for example, a mole of Chlorine is 71 grams, because a Chlorine molecule has two atoms.  This led to the [[Ideal Gas Law|Universal Gas Law]] or Ideal Gas Law:

In the 1810s, Gay-Lussac and Avogadro made an amazing discovery:  The mysterious constant is just the molecular weight of the gas, if the amount of gas is measured in the right units.  The right unit to use is the ''mole'', which is the mass, in grams, that matches the molecular weight of the gas.  (By then atomic weights and molecular weights were beginning to be understood.)  So, for example, a mole of Chlorine is 71 grams, because a Chlorine molecule has two atoms.  This led to the [[Ideal Gas Law|Universal Gas Law]] or Ideal Gas Law:

:<math>PV = nRT\,</math>

:<math>PV = nRT\,</math>

where <math>n\,</math> is the amount of gas, measured in moles, and <math>R\,</math> is the ''Universal Gas Constant'' of 8.314 joules per Kelvin.  A mole has to be defined as that amount, in grams, equal to the molecular weight of the gas.  This required that the molecular weight of diatomic gases, like Hydrogen, Nitrogen, Oxygen, and Chlorine, be twice the atomic weight, because the molecules have two covalently bound atoms.  Inert gases, like Helium and Neon, have only one atom per molecule.  For something like Ammonia vapor (NH₃), the molecular weight is 17, the sum of the atomic weights of the atoms.

where <math>n\,</math> is the amount of gas, measured in moles, and <math>R\,</math> is the ''Universal Gas Constant'' of 8.314 joules per Kelvin.  A mole has to be defined as that amount, in grams, equal to the molecular weight of the gas.  This required that the molecular weight of diatomic gases, like Hydrogen, Nitrogen, Oxygen, and Chlorine, be twice the atomic weight, because the molecules have two covalently bound atoms.  Inert gases, like Helium and Neon, have only one atom per molecule.  For something like Ammonia vapor (NH₃), the molecular weight is 17, the sum of the atomic weights of the atoms.

There are a number of ways of stating this.  A mole is [[Avogadro's number]] (6.022x10²³) of molecules.  The gas law can be restated in terms of the number of molecules:

There are a number of ways of stating this.  A mole is [[Avogadro's number]] (6.022x10²³) of molecules.  The gas law can be restated in terms of the number of molecules:

:<math>PV = nkT\,</math>

:<math>PV = nkT\,</math>

where <math>n\,</math> is the number of molecules and <math>k\,</math> is ''Boltzmann's constant'' (1.38x10^-23 joules per kelvin).

where <math>n\,</math> is the number of molecules and <math>k\,</math> is ''Boltzmann's constant'' (1.38x10^-23 joules per kelvin).  It is just the universal gas constant <math>R\,</math> scaled by Avogadro's number.  Since it makes no reference to artificial units like grams, physicists consider it to be more theoretically significant than the gas constant, and it shows up in many physical formulas (quantum mechanics and statistical mechanics, for example) that are not related to gas behavior.

Scientists were now fairly close to figuring out thermodynamics.  They just needed the kinetic theory and statistical mechanics.  They still didn't know why heat only flows "downhill"&mdash;it was still just an observed fact.  And they didn't know why "heat engines", that is, things that turn heat (e.g. steam) into mechanical energy, aren't very efficient.

Scientists were now fairly close to figuring out thermodynamics.  They just needed the kinetic theory and statistical mechanics.  They still didn't know why heat only flows "downhill"&mdash;it was still just an observed fact.  And they didn't know why "heat engines", that is, things that turn heat (e.g. steam) into mechanical energy, aren't very efficient.

==[[Second Law of Thermodynamics]]==

==[[Second Law of Thermodynamics]]==

James Watt's steam engine drew heat from a specific source and converted some of it to useful work; the remainder of the heat was transferred to a cooler reservoir.  In 1824 a French engineer, N.L. Sadi Carnot, proposed the Carnot cycle, consisting of two isothermal processes (involving a constant temperature) and two adiabatic processes (no heat is gained or lost).  The result was, in theory, the most efficient-working heat engine cycle of any kind, one involving processes that must be reversible and involve no change in entropy.  What was discovered in practice was the second law of thermodynamics, which states (in one of its various formulations) that [[entropy]] in an isolated system cannot decrease, and that ''irreversible processes'' can only make it increase.<ref>Gregory H. Wannier, ''Statistical Physics'', John Wiley & Sons, New York, 1966</ref> An equivalent formulation states that heat cannot spontaneously flow from a cooler body to a hotter body.  Clausius stated that ''"It is impossible for a self-acting machine, unaided by external agency, to convey heat from a body at one temperature to another body at a higher temperature."''

James Watt's steam engine drew heat from a specific source and converted some of it to useful work; the remainder of the heat was transferred to a cooler reservoir.  In 1824 a French engineer, N.L. Sadi Carnot, proposed the Carnot cycle<ref>[https://en.wikiversity.org/wiki/Carnot_engine Carnot Engine]</ref>, consisting of two isothermal processes (involving a constant temperature) and two adiabatic processes (no heat is gained or lost).  The result was, in theory, the most efficient-working heat engine cycle of any kind, one involving processes that must be reversible and involve no change in entropy.  What was discovered in practice was the second law of thermodynamics, which states (in one of its various formulations) that [[entropy]] in an isolated system cannot decrease, and that ''irreversible processes'' can only make it increase.<ref>Gregory H. Wannier, ''Statistical Physics'', John Wiley & Sons, New York, 1966</ref> An equivalent formulation states that heat cannot spontaneously flow from a cooler body to a hotter body.  Clausius stated in what is known as the Clausius statement that <ref>S. J. Blundell & K. M. Blundell, ''Concepts in Thermal Physics'', Oxford University Press, New York, 2016</ref>

 

 

 

 

What it meant was heat transfers to cooler temperatures, and not the other way around.  But this was still just a carefully worked out summary of experimental observation.  While such summaries of observation are important for the progress of science, people still didn't know '''why''' this was true.  Nevertheless, the development of Carnot's theory used that observation to explain why heat engines have limited efficiency.

 

Making progress on the theory required the development of the concept of entropy, and the development of statistical mechanics.  To see what entropy is about, consider its thermodynamical definition as a differential.  Entropy is generally symbolized with a capital S, and heat energy with a capital Q.  While defining entropy in terms of its derivative rather than an actual absolute definition may seem to leave something to be desired (it leaves a "constant of integration" unspecified), that generally doesn't matter.  This standard definition is used:

The change in entropy of some object is the change in heat energy divided by the temperature at which the change takes place.  The unit of thermodynamic entropy is the Joule per Kelvin.  This is an "extensive" measure.  To get the entropy for a given substance, independently of the size of the sample, it has to be divided by the size of the sample.  So the unit of entropy for a substance (e.g. ice) is Joules per Kelvin per mole.  Or per gram, or per atom, or per liter, or whatever.

 

Why is this useful?  It captures the fact that heat flows downhill.  Suppose there is a hot cup of coffee in a cooler room.  Heat will flow from the coffee to the room.  By conservation of energy, that is, the first law of thermodynamics, the amount of heat energy flowing out of the coffee is equal to the heat energy flowing into the room.

(These would actually be instantaneous time derivatives.)  Energy is conserved.  But now consider the equation for entropy.  It the coffee is at 310 Kelvins and the room at 290 Kelvins:

Because of the temperature difference, the entropy of both combined went up by 0.0111.  The fact that heat flows downhill may be captured by saying that

This is still just a nicely formulated statement of observations.  To see why this is the correct definition of entropy, and why this law is correct, statistical mechanics must be developed.  This was done by Maxwell, Boltzmann, Clausius, and others during the 19^th century.

What it meant was heat transfers to cooler temperatures, and not the other way around, which led to the concept of entropy.  An idealized formula for an increase in entropy when heat is applied reads:

For a continuation of this, see the [[Second Law of Thermodynamics]] article.

Where <math>S</math> is the state of the system or entropy, <math>q</math> is the added heat, and <math>T</math> is the absolute temperature.  This increase in entropy must be at least <math>q/T</math>, but the entropy change itself (<math> S</math> is always greater.

==[[The Third Law of Thermodynamics]]==

==[[The Third Law of Thermodynamics]]==

Also known as ''Nernst's Law'', states that it is not possible to bring any system to the [[absolute zero]] of temperature in a finite number of operations. Also stated as follows: The entropy of a perfect crystal at absolute zero is zero.

Also known as ''Nernst's Law'', states that it is not possible to bring any system to the [[absolute zero]] of temperature in a finite number of Carnot cycles. Also stated as follows: The entropy of a perfect crystal at absolute zero is zero.

These laws tell us to what constraints ''any'' system is subject. For example, it allows us to calculate the maximum possible efficiency of an [[engine]] once we know the temperature at which it operates.

These laws tell us to what constraints ''any'' system is subject. For example, it allows us to calculate the maximum possible efficiency of an [[engine]] once we know the temperature at which it operates.

The particular properties of a specific system cannot be calculated from these laws alone. More information is required: so-called ''thermodynamic equations of state'' tell us how a particular system will behave under thermodynamic processes. A simple example of such an equation is the [[Ideal Gas Law]] that applies to dilute gases.

The particular properties of a specific system cannot be calculated from these laws alone. More information is required: so-called ''thermodynamic equations of state'' tell us how a particular system will behave under thermodynamic processes. A simple example of such an equation is the [[Ideal Gas Law]] that applies to dilute gases.

== References ==

== References ==