Perfect gas. Equation of state of an ideal gas. Isoprocesses.

Ideal gas, the equation of state of an ideal gas, its temperature and pressure, volume ... a list of parameters and definitions that operate in the corresponding section of physics can be continued for a long time. Today we will talk just on this topic.

What is considered in molecular physics?

The main object that is considered in this section is the ideal gas. The equation of state of an ideal gas was obtained taking into account normal environmental conditions, and we will talk about this a little later. Now let's approach this "problem" from afar.

Let's say we have some mass of gas. Its state can be determined by using three thermodynamic parameters. This, of course, pressure, volume and temperature. The equation of state of the system in this case is the relation formula between the corresponding parameters. It looks like this: F (p, V, T) = 0.

Here, for the first time, we slowly approach the appearance of such a concept as an ideal gas. It is a gas in which interactions between molecules are negligible. In general, this does not exist in nature. However, any highly rarefied gas is close to it. Of the ideal, there is little difference between nitrogen, oxygen and air, which are in normal conditions. To write down the equation of state of an ideal gas, we can use the combined gas law. We obtain: pV / T = const.

Related notion number 1: Avogadro's law

He can tell us that if we take the same number of moles of absolutely any random gas and put them in the same conditions, among which temperature and pressure, then the gases will occupy the same volume. In particular, the experiment was conducted under normal conditions. This means that the temperature was 273.15 Kelvin, pressure - one atmosphere (760 millimeters of mercury or 101325 Pascal). With these parameters, the gas occupied a volume equal to 22.4 liters. Consequently, we can say that for one mole of any gas, the ratio of the numerical parameters will be constant. That is why it was decided to give this figure a designation with the letter R and call it a universal gas constant. Thus, it is equal to 8.31. Dimension J / mol * K.

Perfect gas. The equation of state of an ideal gas and its manipulation

Let's try to rewrite the formula. To do this, write it in this form: pV = RT. Further, we perform a simple action, multiply both sides of the equation by an arbitrary number of moles. We obtain pVu = uRT. Let us take into account the fact that the product of the molar volume by the amount of matter is simply the volume. But the number of moles at the same time will be equal to the private mass and molar mass. This is how the Mendeleev-Clapeyron equation looks. It gives a clear idea of which system constitutes the ideal gas. The equation of state of an ideal gas takes the form: pV = mRT / M.

We derive the formula for the pressure

Let's do some more manipulations with the expressions. For this, we multiply the right-hand side of the Mendeleev-Clapeyron equation and divide by the Avogadro number. Now we are looking closely at the product of the amount of matter on Avogadro's number. This is nothing more than the total number of molecules in the gas. But at the same time, the ratio of the universal gas constant to Avogadro's number will be equal to the Boltzmann constant. Consequently, the formulas for pressure can be written as follows: p = NkT / V or p = nkT. Here, the notation n is the particle concentration.

Ideal gas processes

In molecular physics, there is such a thing as isoprocesses. These are the thermodynamic processes that take place in the system with one of the constant parameters. In this case, the mass of the substance must also remain constant. Let's look at them more specifically. So, the laws of an ideal gas.

The pressure remains constant

This is the law of Gay-Lussac. It looks like this: V / T = const. It can also be rewritten in another way: V = Vo (1 + at). Here, a equals 1 / 273.15 K ^ -1 and is called the "coefficient of volumetric expansion." We can substitute the temperature for both the Celsius scale and the Kelvin scale. In the latter case we obtain the formula V = Voat.

The volume remains constant

This is the second law of Gay-Lussac, more often called the law of Charles. It looks like this: p / T = const. There is another formulation: p = po (1 + at). Transformations can be carried out in accordance with the previous example. As can be seen, the laws of an ideal gas are sometimes quite similar to each other.

The temperature remains constant

If the temperature of an ideal gas remains constant, we can obtain the Boyle-Mariotte law. It can be written in this way: pV = const.

Associated notion No. 2: partial pressure

Suppose we have a vessel with gases. It will be a mixture. The system is in a state of thermal equilibrium, and the gases themselves do not react with each other. Here, N will denote the total number of molecules. N1, N2 and so on, respectively, the number of molecules in each of the components of the available mixture. We take the pressure formula p = nkT = NkT / V. It can be opened for a specific case. For a two-component mixture, the formula takes the form: p = (N1 + N2) kT / V. But then it turns out that the total pressure will be summed up from the partial pressures of each mixture. So, it will have the form p1 + p2 and so on. This will be partial pressures.

What is it for?

The formula obtained by us indicates that the pressure in the system is on the side of each group of molecules. By the way, it does not depend on others. This was used by Dalton in formulating a law, named after him in his honor: in a mixture where the gases do not react chemically with one another, the total pressure will be equal to the sum of the partial pressures.