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→The Third Law of Thermodynamics
There are a number of ways of stating this. A mole is [[Avogadro's number]] (6.022x10<sup>23</sup>) 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]] (6.022x10<sup>23</sup>) 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<sup>-23</sup> joules per kelvin).
where <math>n\,</math> is the number of molecules and <math>k\,</math> is ''Boltzmann's constant'' (1.38x10<sup>-23</sup> 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"—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"—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.
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:
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:
::<math>dS = dQ/T</math>
::<math>dS = dQ/T</math>
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.
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.
::<math>dQ_{coffee} = -50\qquad\qquad\qquad\qquad dQ_{room} = 50</math>
::<math>dQ_{coffee} = -50\qquad\qquad\qquad\qquad dQ_{room} = 50</math>
==[[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.