Question

Under what condition do real gas fail to obey Charles law

Answer 1

Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is:


An animation demonstrating the relationship between volume and temperature

Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant kB =
R
/
NA
=
n R
/
N
(in each law, properties circled are constant and properties not circled are variable)
When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.[1]

This relationship of direct proportion can be written as:

V
∝
T
{\displaystyle V\propto T}
So this means:

V
T
=
k
,
o
r
V
=
k
T
{\displaystyle {\frac {V}{T}}=k,\quad or\quad V=kT}
where:
V is the volume of the gas,

T is the temperature of the gas (measured in kelvins),

and k is a non-zero constant.

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:

V
1
T
1
=
V
2
T
2
or
V
2
V
1
=
T
2
T
1
or
V
1
T
2
=
V
2
T
1
.
{\displaystyle {\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}\qquad {\text{or}}\qquad {\frac {V_{2}}{V_{1}}}={\frac {T_{2}}{T_{1}}}\qquad {\text{or}}\qquad V_{1}T_{2}=V_{2}T_{1}.}
The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.