An ideal gas, the equation of state of an ideal gas, its temperature and pressure, volume ... the list of parameters and definitions that are used in the corresponding section of physics can be continued for a rather long time. Today we’ll talk about this topic.
What is considered in molecular physics?
The main subject discussed 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 get to this “problem” from afar.
Suppose we have some mass of gas. Its condition can be determined using three parameters of a thermodynamic nature. This, of course, is pressure, volume and temperature. The equation of state of the system in this case will be the formula for the relationship between the corresponding parameters. It looks like this: F (p, V, T) = 0.
Here, for the first time, we are slowly getting closer to the emergence of such a concept as ideal gas. It is called 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. Nitrogen, oxygen and air under normal conditions are not much different from ideal. To write the equation of state of an ideal gas, we can use the combined gas law. We get: pV / T = const.
Related Concept # 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 under the same conditions, including temperature and pressure, the gases will take the same volume. In particular, the experiment was conducted under normal conditions. This means that the temperature was 273.15 Kelvin, the pressure was one atmosphere (760 millimeters of mercury or 101325 Pascals). With these parameters, the gas occupied a volume equal to 22.4 liters. Therefore, we can say that for one mole of any gas the ratio of the numerical parameters will be a constant value. That is why it was decided to give this figure a designation with the letter R and call it the universal gas constant. Thus, it equals 8.31. Dimension J / mol * K.
Perfect gas. The equation of state of an ideal gas and its manipulations
Let's try to rewrite the formula. To do this, we write it in this form: pV = RT. Next, we perform a simple action, we multiply both sides of the equation by an arbitrary number of moles. We get pVu = uRT. Let us take into account the fact that the product of the molar volume by the amount of substance is simply volume. But the number of moles will simultaneously be equal to the quotient of the mass and the molar mass. This is what the Mendeleev-Clapeyron equation looks like . It gives a clear idea of which system an ideal gas forms. The equation of state of an ideal gas will take the form: pV = mRT / M.
We derive the formula for pressure
Let's do some more manipulation of the resulting expressions. To do this, we multiply the right-hand side of the Mendeleev-Clapeyron equation and divide by the Avogadro number. Now carefully look at the product of the amount of substance by the Avogadro number. This is nothing more than the total number of molecules in a gas. But at the same time, the ratio of the universal gas constant to the Avogadro number will be equal to the Boltzmann constant. Therefore, formulas for pressure can be written as follows: p = NkT / V or p = nkT. Here, the designation n is the concentration of particles.
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 should also remain constant. Let's look at them more specifically. So, the laws of ideal gas.
Pressure remains constant
This is the law of Gay Lussac. It looks like this: V / T = const. It can be rewritten in another way: V = Vo (1 + at). Here a is equal to 1 / 273.15 K ^ -1 and is called the "coefficient of volume expansion". We can substitute the temperature both on the Celsius scale and on the Kelvin scale. In the latter case, we obtain the formula V = Voat.
The volume remains constant
This is the second Gay-Lussac law, more commonly referred to as Charles's law. It looks like this: p / T = const. There is another formulation: p = po (1 + at). Conversions can be carried out in accordance with the previous example. As you can see, 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, then we can obtain the Boyle-Mariotte law. It can be written like this: pV = const.
Related Concept # 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 existing mixture. We take the pressure formula p = nkT = NkT / V. It can be disclosed for a specific case. For a two-component mixture, the formula will take 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 the partial pressure.
What is it for?
The formula we obtained indicates that the pressure in the system is exerted by each group of molecules. By the way, it does not depend on others. Dalton took advantage of this when formulating the law, later named after him: in a mixture where gases do not react chemically with each other, the total pressure will be equal to the sum of the partial pressures.