Charles' Law
Charles' law states that, at a constant pressure, the volume
of a
mixed amount of gas is directly proportional to its absolute
temperature:
= k 

Where
k is a constant unique to the amount of gas and pressure. Just
as with Boyle's law, Charles' law can be expressed in its more
useful form:
= 

The subscripts 1 and 2 refer to two different sets of conditions, just
as with Boyle's law.
Why must the temperature be absolute? If temperature is
measured on a Celsius (non absolute) scale, T can be negative. If we
plug negative values of T into the equation, we get back
negative volumes, which cannot exist. In order to ensure that only
values of V≥ 0 occur, we have to use an absolute temperature
scale where T≥ 0. The standard absolute scale is the Kelvin
(K) scale. The temperature in Kelvin can be calculated via T_{k} = T_{C} + 273.15. A plot of the temperature in Kelvin vs. volume
gives :
Figure %: Temperature vs. Volume
As you can see from , Charles' law predicts
that volume will be zero at 0 K. 0 K is the absolutely lowest
temperature possible, and is called absolute zero.
Avogadro's Law
Avogadro's law states that the volume of a gas at constant
temperature and pressure is directly proportional to the number of
moles of gas present. It's mathematical representation follows:
k is a constant unique to the conditions of
P and
T.
n is the
number of moles of gas present.
1 mole (mol) of gas is defined as the amount of gas containing
Avogadro's number of molecules. Avogadro's number (N_{A}) is
1 mol of
any gas at 273 K (0_C) and 1 atm has a volume of
22.4 L. The conditions 273 K and 1 atm are the standard
temperature and pressure (STP). STP should not be confused with the
less common standard atmospheric temperature and pressure (SATP), which
corresponds to a temperature of 298 K and a pressure of 1 bar.
The numbers 22.4 L, 6.022×10^{23}, and the conditions of STP
should be near and dear to your heart. Memorize them if you haven't
already.
The Ideal Gas Law
Charles', Avogadro's, and Boyle's laws are all special cases of the
ideal gas law:
T must
always be in Kelvin.
n is almost always in moles.
R is the gas constant. The value of
R depends on the units
of
P,
V and
n. Be sure to ask your instructor which values you
should memorize.
Units  Value of R 
 0.08206 
 8.314 
 8.314 
 1.987 
 62.36 
You can think of
R as a converter that changes the units on the right
side of the above equation to the units on the left side of
the "=" sign. The values
0.0821 and
8.314 get the most use. Memorizing them will make your
life easier.