The natural phenomena and processes surrounding us are quite complex. For their accurate physical description, a cumbersome mathematical apparatus should be used and a large number of significant factors should be taken into account. To avoid this problem, some simplified models are used in physics, which greatly facilitate the mathematical analysis of the process, but practically do not affect the accuracy of its description. One of them is the ideal gas model. Let's consider it in the article in more detail.
The concept of perfect gas
An ideal gas is an aggregate state of a substance, which consists of material points that do not interact with each other. Let us explain in more detail a similar definition.
Firstly, we are talking about material points as objects that make up an ideal gas. This means that its molecules and atoms do not have a size, but have a certain mass. This bold approximation can be made taking into account the fact that in all real gases at low pressure and high temperatures, the distance between the molecules is much larger than their linear dimensions.
Secondly, molecules in an ideal gas should not interact with each other. In fact, such interactions always exist. So, even atoms of noble gases experience dipole-dipole attraction. In other words, van der Waals interactions are present. Nevertheless, compared with the kinetic energy of rotation and translational movement of molecules, these interactions are so insignificant that they do not affect the properties of gases. Therefore, they can not be considered in solving practical problems.
It is important to note that not all gases, in which the density is low and the temperature is high, can be considered ideal. In addition to van der Waals interactions, there are other, stronger types of bonds, for example, hydrogen bonds between H 2 O molecules, which lead to a gross violation of the conditions of gas ideality. For this reason, water vapor is not an ideal gas, but air is it.
The physical model of an ideal gas
This model can be represented as follows: suppose that a gas system contains N particles. It can be atoms and molecules of various chemicals and elements. The number of particles N is large, therefore, a unit of “mole” is usually used to describe it (1 mol corresponds to the Avogadro number). All of them move in a certain volume V. Particle motions are chaotic and independent of each other. Each of them has a certain speed v and moves along a straight path.
Theoretically, the probability of collision between particles is practically zero, because their size is small compared to interparticle distances. However, if such a collision occurs, then it is absolutely elastic. In the latter case, the total momentum of the particles and their kinetic energy are conserved.
The considered ideal gas model is a classical system with a huge number of elements. Therefore, the velocities and energy of particles in it obey the Maxwell-Boltzmann statistical distribution. Some particles have low speeds, others - large. At the same time, there is a certain narrow speed limit in which the most probable values of this quantity lie. The velocity distribution diagram of nitrogen molecules is shown schematically below.
Kinetic theory of gases
The model of ideal gases described above uniquely determines the properties of gases. This model was first proposed by Daniel Bernoulli in 1738.
Subsequently, it was developed to the modern state by August Kroenig, Rudolf Clausius, Mikhail Lomonosov, James Maxwell, Ludwig Boltzmann, Marian Smoluchowski and other scientists.
The kinetic theory of fluid substances, on the basis of which the ideal gas model is constructed, explains two important macroscopic properties of the system based on its microscopic behavior:
- The pressure in the gases is the result of the collision of particles with the walls of the vessel.
- The temperature in the system is the result of the manifestation of the constant movement of molecules and atoms.
Let us reveal in more detail both conclusions of the kinetic theory.
Gas pressure
The ideal gas model involves constant random movement of particles in the system and their constant collision with the walls of the vessel. Each such collision is considered absolutely elastic. The particle mass is small (≈10 -27 -10 -25 kg). Therefore, it cannot create a lot of pressure in a collision. Nevertheless, the number of particles, and hence the collisions, is huge (≈10 23 ). In addition, the mean square velocity of the elements is several hundred meters per second at room temperature. All this leads to the creation of tangible pressure on the walls of the vessel. It can be calculated using the following formula:
P = N * m * v cp 2 / (3 * V),
where v cp is the mean square velocity, m is the particle mass.
Absolute temperature
According to the ideal gas model, the temperature is uniquely determined by the average kinetic energy of a molecule or atom in the system under study. We can write the following expression, which relates kinetic energy and absolute temperature for an ideal gas:
m * v cp 2/2 = 3/2 * k B * T.
Here k B is the Boltzmann constant. From this equality we obtain:
T = m * v cp 2 / (3 * k B ).
Universal equation of state
If we combine the above expressions for absolute pressure P and absolute temperature T, then we can write the following equality:
P * V = n * R * T.
Here n is the amount of substance in moles, R is the gas constant introduced by D.I. Mendeleev. This expression is the most important equation in the theory of ideal gases, since it combines three thermodynamic parameters (V, P, T) and is independent of the chemical characteristics of the gas system.
The universal equation was first experimentally derived by the French physicist Emil Clapeyron in the 19th century, and then reduced to the modern form by the Russian chemist Mendeleev, therefore, at present it bears the names of these scientists.