Subsection 4.2.2 Kinetic Theory of Gases
The nature of gas is completely different than solids and liquids. Gas takes up the entire volume of the container and can be compressed easily. Gas pressure increases or decreases as the temperature of the container changes. It diffuses (or leaks out) to the air if the container is left open. On such experiences, Kinetic theory of gas is developed to explain the nature of heat and the motion of particles associated with heat energy. According to this theory, gas is composed of large numbers of very tiny particles called molecules. These molecules are always in random motion at all possible directions and speeds which increases with the increase of temperature. In gases, the molecules are very far away from each other than in solids and liquids and have negligibly small force of attraction between them. Hence they can move freely anywhere within the available space. This explains why a gas has no definite shape and size. To understand the more general behavior of gases the kinetic theory of ideal gases is postulated as
- All gases are made up of molecules. Molecules are identical, rigid, and perfectly elastic moving in random directions with all possible velocities.
- The molecules are very far away from each other but they collide with each other and with walls of the container.
- All the collisions are elastic, but time spent during each collision is negligibly small compared to the time spent between the collisions.
- Molecules do not interact with each other (no intermolecular force of attraction) except during a collision.
- The average kinetic energy of the molecules of any gas depends only on the temperature.
Ideal gas is a hypothetical gas of negligible molecular size and have no interactions among their molecules. In practice, a very dilute gas with extremely large volume of container space can be considered as an ideal gas. Remember the real gas molecules has definite size and may interact with each other. Hence these postulates are just a very simplified model to understand gas laws and need modification for real gas behaviors. To experience the general behavior of gas please play with the simulation link here. gas laws
1
phet.colorado.edu/sims/html/gas-properties/latest/gas-properties_en.htmlSubsubsection 4.2.2.1 The Gas Laws
From the experience of factors affecting gas pressure the ideal gas law is defined below. Ideal Gas Law or also called equation of state. It is found that the pressure, \(p\) of the gas is directly proportional to number of molecules, \(N\) and the absolute temperature, \(T\) and inversely proportional to the volume, V of the gas. That is,
\begin{align*}
p \amp \propto \frac{NT}{V} \\
p \amp = \frac{NkT}{V}
\end{align*}
where \(k\) is proportionality constant. Therefore
\begin{equation}
p V = NkT\tag{4.2.7}
\end{equation}
For \(n\) mole of gas, the above equation turns into
\begin{equation}
pV = nRT\tag{4.2.8}
\end{equation}
this equation is known as equation of state. Here, \(n\) is number of mole of gas in a container and \(R=8.314 \,J/mol/K\) is universal gas constant.
If T is constant in this equation then it is called Boyle’s Law
\begin{equation*}
pV= constant.
\end{equation*}
If \(p\) is constant in this equation then it is called Charle’s Law
\begin{equation*}
\frac{V}{T}= constant.
\end{equation*}
