Question

Explain Charles’s law on the basis of the kinetic theory of matter.

Answer 1

Hint: The kinetic theory of matter is based on five postulates or assumptions that explain the macroscopic properties of gases with relation to their microscopic properties. Charles’s law explains the dependence of volume of a gas on the temperature at constant pressure.

Complete Step by step answer:
The five postulates of kinetic theory of matter are explained below:
1.In an ideal gas there is no interaction between the molecules of the gases, hence they do not exert intermolecular forces on each other.
2.The volume of gas is equal to the volume of the container in which it is present, as individual gas molecules are very small in size and the volume occupied by individual gas molecules is negligible as compared to the gas.
3.The gas molecules are always in random motion and they travel in straight lines, until they collide with other gas molecules or the walls of the container.
4.The collision between gas molecules is completely elastic, that is, the total kinetic energy is conserved during collision.
5.The average kinetic energy of the gas molecules is directly proportional to the temperature of the gas, which means that at absolute zero temperature the average kinetic energy of the molecules will be zero and all molecular motion will cease.

Charles’s law is one of the gas laws which explains that at constant pressure, the temperature and volume of a gas are directly proportional to each other.
According to kinetic theory, as temperature rises the kinetic energy of gas also increases proportionally. Due to the increase in the kinetic energy of the gas, the molecules will start moving rapidly with an increase in the number of collisions, in order to maintain constant pressure, there must be an increase in the volume of the gas so as to keep the molecules apart.
We know, $PV = nRT$
As ‘n’ and ‘R’ are constant, then at constant ‘P’,
$V \propto T$

So, $\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$

Note: Another important gas law is Boyle's law, which states that at constant temperature, the pressure of the gas is inversely proportional to the volumes of the gas. That is, an increase in the pressure of the gas will lead to a decrease in the volume and vice versa.