[Physics Class Notes] on Kinetic Theory of Gases Assumptions Pdf for Exam

Kinetic theory of gasses is a theory based on a simplified molecular or particle description of gas and from this many gross properties of the gas can be derived. It is a theory that derived that the particles in a gas move freely and rapidly along straight lines but often collide, resulting in variations in their velocity and direction. Pressure is also interpreted as arising from the impacts of these particles on the walls of a container. The greater the density of a gas, the more will be the number of collisions between molecules and the surface and the greater the pressure exerted. 

When the volume of a certain mass of gas is reduced, or when more gas is pumped into a vessel then the pressure is increased. The speed of the molecules increases by the increment of the temperature of the gas, causing an increment in both the number and the momentum imparted by each collision. This leads to the increment in pressure of a gas with an increase in temperature. The kinetic theory of gasses explains the macroscopic properties of gasses and the formula derived from it as well, the properties are volume, pressure, and temperature.

PV = nRT

Kinetic Theory of Gas – Assumptions

The Kinetic theory of gas has various assumptions like: 

• The kinetic gas is composed of a large number of identical molecules that are moving in random directions, separated by distances that are large compared with their size.

• The molecules undergo perfectly elastic collisions or no energy loss with one another and with the walls of the container but they do not interact.

• The transfer of this kinetic energy between molecules is heat. These theories bring the properties of gasses within the particular range of mathematical treatment.

• The separation between all the molecules is comparatively greater than the size of the molecules.

• All the molecules in a kinetic gas sample obey the laws of motion.

• If a kinetic gas sample is left for a sufficient time, it eventually comes to a steady state. Therefore the density of molecules and the distribution of molecules are independent of position, distance, and time.
  

Postulates of The Kinetic Theory of Gas

The kinetic theory of gas consists of various postulates like :

• The particles in a kinetic gas are in constant or random motion.

• The combined volume of all the particles is negligible.

• The particles simply no forces on one another.

• Any type of collision between the particles is completely elastic.

• The kinetic energy of the particles is directly proportional to the temperature in kelvins.
  

Gases are an exciting subject to study, which can be easily understood by taking into consideration the action of individual molecules. You can also understand more about gases by taking into consideration the gases’ large-scale action. However, to further study how molecules act in different situations, you need a theoretical model. This is where the Kinetic theory of gases comes into the picture. Now, the most obvious question is, what do you mean by the kinetic theory of gases? It is the conceptual model that assumes that the size of molecules is very small when compared to the distance between these molecules. These molecules are constantly moving, and since the distance between them is less, they collide with each other. 

Basics of Kinetic Theory of Gases

As per the basics of the kinetic theory of gases, the molecules move in random motion and keep on colliding with each other as well as the walls of the container they are kept in. Since these collisions remain elastic in nature, both the total momentum as well as total kinetic energy are conserved easily. Thus, you will find that neither the energy is preserved nor lost during this collision of molecules.

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(In the image above, you can see the kinetic theory of gases formula. The different aspects of the formula are P = pressure of gas; V = volume of gas;  T = temperature; N = moles of gas which are present; and R is the constant, which is known as the universal gas constant)

Here: PV = nRT;

Where:

P is the pressure of gas;

V is the volume of the gas;

T is the temperature which is measured in kelvin;

N is regarded as the moles of gas that are present;

R is the constant, which is known as the universal gas constant.

Postulates of Kinetic Theory of Gases

The theory related to gases based on molecular motion is known as the kinetic theory of gases. However, like any other theory, there are some postulates of the kinetic theory of gases as well. Let us read in detail about these postulates of the kinetic theory of gases:

• During the collision process, the molecules cannot lose any kind of kinetic energy. Thus, it can be easily said that these said collisions are perfectly elastic. 

• You can find ample space between these moving molecules, which leads to continuous motion between them.

• The molecules present in a gas are actually very minute and distanced from each other. This implies that the volume occupied by a particular gas is just empty space and nothing else.

• The collision occurs between molecules among each and with the walls of the container they are kept in. This collision is responsible for the gas pressure.
  

Assumptions of Kinetic Theory of Gases

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(The image represents the assumptions of the kinetic theory of gases. There are 5 main assumptions as mentioned below)

• These gas molecules move in constant random motion, and most of these molecules are moving in one single direction than other molecules.

• During the process, these said molecules present in the gas are not exerting any kind of attractive or repulsive forces on each other. During the collision, they do exert pressure on each other. However, when they are not colliding, they keep on moving in straight lines.

• The division between these molecules is much more in size than the molecules’ actual size.

• All kinds of collisions occurring between these molecules, as well as between the molecules and the wall, are elastic in nature.

• All these molecules present in the said gas diligently obey Newton’s law of motion.
  

These assumptions of the kinetic theory of gases make sure that the gas characteristics lie within the range of mathematical calculations.

More About Kinetic Theory of Gases

It was in the 19th century that scientists, by the name of James Clark Maxwell, Clausius, and Rudolph, worked upon the development of the kinetic theory of gases to explain the concerned gasses’ behavior. As per the theory, gas is considered to be a complete collection of minute, hard spheres that can interact with each other as well as the container in which the gas is contained. 

As per the kinetic theory, the pressure exerted by the gas is the result of collisions taking place between the gas molecules as well as the container walls where they exist. Further, the temperature of the gas is in relation to the gas molecules’ average moving speed. However, remember that at a constant temperature, the molecules’ speed actually remains constant. Now, if anyone reduces the container’s volume, the molecules will enjoy less distance for travelling, and thus, they would be hitting the container’s wall causing higher pressure. On the other hand, if the container’s volume increases, the molecules will hit the walls of the container with less speed, resulting in lower pressure.