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→First Law of Thermodynamics
Putting these together, we get, for a given sample of gas:
Putting these together, we get, for a given sample of gas:
:<math>PV = XT\,</math>
:<math>PV = XT\,</math>
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.
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. 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:
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: