Question

The average kinetic energy of all the molecules is assumed to be:
A. Inversely proportional to the absolute temperature of the gas.
B. Directly proportional to the absolute temperature and size of the gas.
C. Directly proportional to the absolute temperature of the gas.
D. Not related to the absolute temperature of the gas

Answer 1

Hint: The average kinetic energy of a molecule is given by, $K.E. = \dfrac{3}{2}kT$ where $k$ is the Boltzmann constant and $T $is the absolute temperature of the gas.

Complete step by step solution:
We already know that, in order to know the properties of gases and the gas laws theoretically, a theoretical model of gas was given which is known as the “Kinetic molecular theory of gases”.
There are several postulates of Kinetic Theory of Gases which are as follows:
1. All molecules of a particular gas are identical in mass and size and this differs from gas to gas.
2. The molecules of a gas are separated from each other by large distances so that the actual volume of the molecules is negligible compared to the total volume of gas.
3. It was assumed that the force of attraction between molecules is negligible.
4. The molecules were supposed to be moving in different directions with different velocities.
5. The pressure exerted on walls of containers is due to the bombardment of molecules on walls of containers.
6. The collision between molecules was assumed to be perfectly elastic so that no energy is wasted during collision.
7. Since molecules are moving with different velocities, this means that they possess different kinetic energies. However, the average kinetic energy of molecules of a gas is directly proportional to the absolute temperature of gas. This has emerged as a result of the fact that when the temperature of gas is raised, the molecules start moving faster. Thus, their individual kinetic energy increases and hence the average kinetic energy also increases.

Therefore, on looking at postulate 7 we can say that option C is the correct answer.

Note: It should be remembered that the average kinetic energy of a molecule of any particular gas only depends on the absolute temperature of the gas and doesn’t depend on the size of molecule of the given gas.