The expansion of a gas – absolute zero and Charles’ Law
These effects are all happen because a
gas tries to expand when it is heated.
When the gas is heated the molecules in
the gas move round faster. They are being given energy in the form of heat and
this appears as the extra kinetic energy of the gas molecules. The molecules
bang into each other and into the walls of the container more violently and
this increases the pressure and so the gas tries to expand.
If we allow the gas to expand the pressure
can be kept constant and we can investigate the connection between the
temperature of the gas and its volume.
 |
| Graph (1) |
This can be done using the simple apparatus
shown in the diagram.
The tube and the thermometer are immersed
in water which is then heated.
The trapped air in the tube expands and the volume at different temperatures can be recorded. If a graph of volume
against temperature is plotted you should get a result similar to graph 1.
(Notice that the pressure of the trapped
air stays the same – atmospheric pressure)
However if we draw the line back it to
the point where the theoretical volume
of the gas is zero it will cut the
temperature
axis at a point well below 0oC.
We call this point ABSOLUTE ZERO.
We could then measure all temperatures by
starting at this point and if we do then we will get a graph like graph 2.
If the
experiment has been done really carefully absolute zero turns out to be about
–273oC. This is the coldest that it is possible to get.
 |
| Graph (2) |
The Kelvin (or absolute) temperatue scale
It is useful to
define a new scale of temperature starting at absolute zero. The size of the
degrees is the same as those for the Celsius scale but the numbers are different.
We call this scale the ABSOLUTE or KELVIN temperature scale. Temperatures on
this scale are given the symbol K.
So for example
absolute zero (-273oC) become 0 K on the Kelvin scale. The freezing
point of water (0oC) becomes 273 K on the Kelvin scale. The boiling
point of water becomes 373 K on the Kelvin scale and so on. To change from
Celsius to Kelvin you simply ADD 273 and to change from Kelvin to Celsius you
simply take 273 away from the temperature.
When working
with gas equations like the one below you must ALWAYS use the Kelvin
scale.
In deep space
far from any stars the temperature is still 3K or –270oC!).
Charles’ Law
The equation for
the line was first suggested by the French Physicist Jacques Charles in 1787.
It states that
for an ideal gas:
Volume of the gas/Absolute temperature of the gas = constant
As long as the
pressure of the gas is kept constant.
If the gas is heated so that its volume
changes from volume 1 to volume 2 while its temperature changes from
temperature 1 to temperature 2 then:
Volume 1/Temperature 1 = Volume 2/Temperature 2
Example problem
A sample of air with a volume of 3 m3 at 27oC (300K) is heated to a temperature of 100oC (373K). If the pressure of the air is kept the same what is the new volume of the sample of air. 3/300 = V2/373 Therefore: V2 = 373/100 = 3.73 m3
Note: An ideal gas is one which cannot be liquefied by simply
increasing the pressure. The molecules of the gas are supposed to exert no
force on each other. If you want to learn more about ideal gases then have a
look at the 16-19 text section.
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