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→First Law of Thermodynamics
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 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,
:<math>PV = constant</math>
:<math>PV = constant</math> where the constant depends on the amount and type of the gas sample
[[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,
[[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>
:<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.
Putting these together, we get, for a given sample of gas
Putting these together, we get, for a given sample of gas:
:<math>PV = ZT</math>
:<math>PV = XT\,</math>
Where Z is some constant that is characteristic of the gas sample. It's easy to see that Z is proportional to the amount of gas (2 grams of gas will have twice the volume of 1 gram). So Z is actually the amount of gas, measured in some convenient units (grams, moles, molecules), time 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), timea 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.
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. A good choice for the right unit 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.) This led to the [[Ideal Gas Law|Universal Gas Law]] or Ideal Gas Law:
:<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 (NH<sub>3</sub>), 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]] (6.022x10<sup>23</sup>) of molecules. The gas law can be restated in terms of the number of molecules:
:<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).
==[[Second Law of Thermodynamics]]==
==[[Second Law of Thermodynamics]]==