Universal Gas Law

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 ,
:

V \

is the Volume ,
:

n \

is the number of Moles of gas,
:

R \

is the Gas Constant , and
:

T \

is the Temperature .

The ideal gas law is most accurate for monoatomic 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.

PROOF

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{kPa} \,

t_0 = 290 \ \mathrm{K}

If this gas undergoes an Isobaric Process , its final volume will be:

:

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

and its temperature will be

t

.

If it then undergoes an Isothermal Process :

:

p_0v' = pv \,

So:

:

pv = p_0v' \,

;
:

pv = p_0v_0(1 + \alpha t) \,

;
:

pv = {rac{p_0 v_0}{290 \ \mathrm{K}}}T

;

where

{rac{p_0 v_0}{290 \ \mathrm{K}}}

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 \,

Information About

Universal Gas Law