Similar to the liquids gases also has no specific area and
length and hence there are no linear and areal expansions for a gas. We need
not worry about the apparent expansion and real expansion in the case of the
gases. It is simply because the volume expansion of the gases so large such
that it is not going to make a difference whether it is apparent expansion or
real expansion.
While studying the expansion of solids and liquids we need to
worry about the impact of pressure. But pressure plays important role during
the expansion or the contraction of the gases and we cannot ignore the
parameter. Studying the variation of the volume both with respect to
temperature and pressure simultaneously leads to unwanted confusion. That’s why
we will be keeping one of the parameter constant and steady the other two
parameters.
Hence gases have two types of expansion coefficients. They
are volume expansion coefficient of a gas at constant pressure and pressure
expansion coefficient of a gas at constant volume.
Volume expansion coefficient of a gas at constant pressure is
defined as the ratio of change in the volume of the gas to its original volume
at 0°C per 1°C rise in temperature at constant pressure.
Pressure expansion coefficient of a gas at constant volume is
defined as the ratio of change in the pressure to its original pressure at 0°C
per 1° c rise in temperature at constant volume.
We can find the relation between these two coefficients as
shown below. It is noticeable that both are identical. Irrespective of any of
the gas, the expansion coefficients are same.
When a graph is drawn between the volume and temperature at
the constant pressure, it can be noticed that with the increase of the
temperature volume of the gas also increases. With the decrease of the
temperature volume starts decreasing and at a temperature -273°C volume of any
gas becomes zero. This particular temperature is called as absolute zero
temperature. This is taken like a reference to design a scale and the scale is
called as absolute scale or Kelvin scale.
Boyle’s law
At constant temperature, for a given mass of the gas pressure
is inversely proportional to volume.
Boyle’s law is not treated like a fundamental law because it
is true only under certain conditions like mass has to be constant.
Charles law
At constant pressure, volume of the gases directly
proportional to absolute temperature and vice versa.
A gas which satisfies all gas laws at all temperatures and
pressures is called an ideal gas. No gas in real life is ideal. All the
existing gases are called real gases, which obey gas laws only at high
temperatures and low pressures.
We can derive the equation for the ideal gas equation as
shown below.
While verifying the Boyle’s law we can verify has the product
of pressure and volume equal to constant. When the gas is taken in a uniform
tube of certain cross-section we can write the volume of the gases the product
of area and length. As the area is constant we can verify the Boyle’s law by
proving that the product of pressure and length is also constant.
Problem and solution
If the pressure of a gas is increased by 10% at constant
temperature what happens to its volume ?
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