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Sunday, February 22, 2015

Perfect Gas Law

In the kinetic theory of gases, an ideal gas is one in which the individual molecules are sufficiently far apart that the short range force that acts between them can be ignored. Collisions between molecules are assumed to be perfectly elastic.

Laboratory experiments have shown that for such a gas there is a simple equation of
state relating the pressure p, absolute temperature T, and volume V. For m kilograms of
gas, this equation may be written
pV = mRT,
where R is a constant for the particular gas. R is called the gas constant and has units of
Joules per degree per kilogram.

We define a kilogram-molecular weight, or kilomole (abbreviated kmole) of a material
as its molecular weight expressed in kilograms. (Older texts define molecular weight as
the molecular weight expressed in grams).

For example, the molecular weight of water is 18.016, and therefore one kilomole of water is 18.016 kg of water. The number of kilomoles n in mass m (in kilograms) of material is given by

n = m/M.

Where M is the molecular weight. One kilomole of any material is equal to the weight of a single molecule (in kg) times the number of molecules, N. This number is called Avogadro's number and has the value 6.022 ×1026 (for a kmol of substance).

Avogadro hypothesized that gases containing the same number of molecules occupy the same volume at the same pressure and temperature. This implies that for one kilo mole of any gas
pV = MRT

Accordingly, R* = MR is a universal constant for all gases. It is called the universal gas constant and has the value 8314.3 J deg −1 kmol −1 .