GAS LAWS AND KINETIC THEORY
IDEAL GAS LAW
Boyle's Law: For a gas at a constant temp erature the pro duct of pressure and volume is constant:
PV = constant,or P V = P V .
1 1 2 2
Law of Charles and Gay-Lussac: For a gas at a constant pressure the volume is prop ortional to the
temp erature: V=T = constant,or V =V = T =T .
1 2 1 2
Rememb er: The temp erature MUST b e in Kelvin!!
corresp onds to the quantity of gas in mol es.
The number of mol es is de ned as the ratio of the total mass M of the gas and the Molecular Mass
in g =mol of the gas: n = M=M ol ecul ar M ass. The Molecular mass of a gas is di erent for each
gas. For example: Molecular oxygen O =32g =mol , Helium He= 4g =mol etc.
1 mol e of any gas contains the same numb er of particles.
This number is N =6:02 10 M ol ecul es=mol and is called Avogadro's numb er.
KINETIC THEORY OF GASES
The temp erature of a gas can b e related to the internal motion of the molecules.
The ideal gas approximation yields: PV =2=3N KE , where KE is the mean kinetic energy of an
individual molecule and N is the total numb er of molecules in the gas.
The internal energy U of a gas is de ned as U = N KE and thus PV =2=3U .
KE =3=2kT , where The relation b etween the mean kinetic energy and the temp erature is given by