The Ideal Gas Law equation is derived from the three gas laws. Explain the
THREE gas laws by providing mathematical equations showing the
relationship between the relevant quantities.
The main laws for ideal gases used in thermodynamics are Boyle's law - Mariotte, Gay-Lussac's law, Charles's law and Avogadro's law. These laws establish relationships between the main parameters of gases - pressure, volume, temperature and molecular weight.
Boyle's Law - Mariotte
Boyle's law - Mariotte states that the product of the absolute pressure of a gas and its specific volume in an isothermal process (at constant temperature) is a constant value:
pv = const.
Gay Lussac's Law
Gay-Lussac's law states that at constant pressure (isobaric process), the specific volume of a gaseous substance (volume of constant gas mass) changes in direct proportion to the change in absolute temperatures:
v1 / v2 = T1 / T2.
Charles's law, which is sometimes called the second Gay-Lussac law, is that with a constant specific volume, the absolute gas pressures change in direct proportion to the change in absolute temperatures:
p1 / p2 = T1 / T2.
Avogadro's law states that all gases at the same pressure and temperature contain the same number of molecules in equal volumes. It follows from this law that the masses of two equal volumes of different gases with molecular masses μ1 and μ2 are equal, respectively:
M1 = m1N and M2 = m2N,
where: m1 and m2 - respectively, the mass of one molecule of the considered gases; N is the number of molecules in a given volume.