Question

The kinetic energy of a molecule of a gas is directly proportional to the ____of the gas.

Answer 1

Hint: In the gaseous system, the molecules move constantly and colloid with each other. During the elastic collision, the conservation of the total kinetic energy takes place.
The gas molecules get enlarged when at constant pressure the system is heated.

Complete step by step answer:
The kinetic molecular theory helps to determine the physical properties of gas molecules.
It is used to determine the gas laws i.e, Boyle’s law, and Charles law.
The gas is formed of molecules which are parted from each other by an average distance.
As we know that in the gaseous system, most of the volume inhabited by the gas molecules is vacant. Due to the presence of a large volume, the gas molecules move in a random motion and result in elastic collisions at normal temperature and pressure.

As the temperature of the system increases, the average velocity of the molecule increases. Due to this collision of the molecules with the wall will exchange larger momentum and thus kinetic energy will be increased.
The molecular motion gets terminated when the temperature is absolute zero.
The kinetic energy can be calculated by the formula shown below.
$K.E = \dfrac{1}{2}m{v^2}$
K.E is the kinetic energy of the gas molecule.
m is the mass of the gas molecule.
v is the magnitude of velocity of the gas molecule.
Therefore, the kinetic energy of a molecule of a gas is directly proportional to the _temperature_ of the gas.


Note:
At the specific given temperature, the pressure inside the container is known by the total number of times the molecules of gas hit the walls of the container. When the gas is compressed by a small volume, then the same amount of molecules of gas will hit the small surface of the container and collision will increase along with the pressure. Thus, with the increase in the kinetic energy of gas molecules, pressure also increases.