yawiki.org entry for Ideal gas law

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The ideal gas law is the equation of state of an ideal gas. The state of an amount of gas is determined by its pressure, volume, and temperature. The equation has the form

$pV = nRT$

where

$p$ is the pressure Pa,

$V$ is the volume m³,

$n$ is the number of moles of gas mol,

$R$ is the gas constant 8.314472 m³·Pa·K^-1·mol^-1, and

$T$ is the temperature in kelvin or rankine K.

The gas constant ("R") is dependent on what units are used in the formula. The value given above, 8.314472, is for the SI units of Pascal-Meters^3 per per mole-Kelvin.

The ideal gas law is most accurate for monatomic gases and is favored at high temperatures and low pressures. It does not factor in the size of each gas molecule or the effects of intermolecular attraction. The more accurate Van der Waals equation takes these into consideration.

    Ideal gas law
        Alternate Forms
            Empirical
            Theoretical
        See also

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Alternate Forms
Considering that the number of moles (

n

) could also be given in mass, sometimes you may wish to use an alternate form of the ideal gas law. This is particularly useful when asked for the ideal gas law approximation of a known gas.
Consider that the number of moles (

n

) is equal to the mass (

m

) divided by the molar mass (

M

), such that:

$n =$

Then, replacing $n$ gives:

$pV =$

In thermodynamics and physics, when something is referred to as specific, it simply means the value per unit mass. In the case of the gas constant, the specific gas constant (

r

) would be

R

divided by the molar mass of the gas in question:

$r =$ or $R = rM$ (where $r$ is the specific gas constant)

Replacing with $r$ in the above formula yields:

$pV = mrT$ (the molar masses cancel) or $pV = nrMT$

Since density (D) equals mass over volume, it is possible to substitute volume for grams over density (V = g/D), and make appropriate changes.

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Empirical

The ideal gas law can be proved using Boyle, Charles and Gay-Lussac laws.

Consider a volume

v_0

of gas. Let its state be defined as:

$p_0 = 100 mathrm ,$

$t_0 = 290 mathrm$

Firstly, If this gas undergoes an isobaric process, its final volume will be:

$v' = v_0(1 + alpha t) ,$

and its temperature will be

t

.

Secondly, If it then undergoes an isothermal process:

$p_0v' = pv ,$

So:

$pv = p_0v' ,$ ;

$pv = p_0v_0(1 + alpha t) ,$ ;

$pv = T$ ;

where

called

R

, is the universal gas constant. Using this notation we get:

$pv = RT ,$

And multiplying both sides of the equation by n (numbers of moles):

$pnv = nRT ,$

Using the symbol

V

as a shorthand for

nv

(volume of n moles) we get:

$pV = nRT ,$

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Theoretical

The ideal gas law can also be derived from first principles using the kinetic theory of gases, if the molecules are assumed to be hard spheres.

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