The main subject of studying the thermodynamics of gas systems is the change in thermodynamic states. As a result of such changes, gas can do work and store internal energy. Let us examine in the article below the different thermodynamic transitions in an ideal gas. Particular attention will be paid to studying the schedule of the isothermal process.
Ideal gases
Judging by the name itself, we can say that 100 percent ideal gases do not exist in nature. However, many real substances satisfy this concept with practical accuracy.
Any gas in which interactions between its particles and their sizes can be neglected is called ideal. Both conditions are satisfied only if the kinetic energy of the molecules will far exceed the potential energy of the bonds between them, and the distances between the molecules will be much larger than the particle sizes.
To determine whether the gas under study is ideal, you can use a simple rule of thumb: if the temperature in the system is higher than room temperature, the pressure is not much different from atmospheric or lower, and the molecules that make up the system are chemically inert, then the gas will be ideal.
Main law
We are talking about the ideal gas equation, which is also called the Clapeyron-Mendeleev law. This equation was written down in the 30s of the XIX century by the French engineer and physicist Emile Clapeyron. After several decades, it was brought to the modern form by the Russian chemist Mendeleev. This equation has the following form:
P * V = n * R * T.
On the left side of the equality is the product of pressure P by volume V, on the right side of the equality is the product of temperature T by the amount of substance n. The value of R is a universal gas constant. Note that T is the absolute temperature, which is measured in kelvins.
The Clapeyron-Mendeleev law was first obtained from the results of previous gas laws, that is, it was based solely on the experimental basis. With the development of modern physics and the kinetic theory of fluids, the ideal gas equation can be deduced from considering the microscopic behavior of particles in the system.
Isothermal process
Regardless of whether this process occurs in gases, in liquids or in solids, it has a very clear definition. Isothermal is the transition between two states in which the temperature of the system is preserved, that is, remains unchanged. Therefore, the graph of the isothermal process in the axes of time (x axis) - temperature (y axis) will be a horizontal line.
Regarding the ideal gas, we note that the isothermal transition for it is called the Boyle-Mariotte law. This law was discovered experimentally. Moreover, he became the first in this area (second half of the XVII century). Each student can get it if he considers the behavior of gas in a closed system (n = const) at a constant temperature (T = const). Using the equation of state, we obtain:
n * R * T = const =>
P * V = const.
The last equality is the Boyle-Marriott law. In physics textbooks you can also find this form of his writing:
P 1 * V 1 = P 2 * V 2 .
In the transition from the isothermal state 1 to thermodynamic 2, the product of volume and pressure remains constant for a closed gas system.
The studied law speaks of inverse proportionality between the quantities P and V:
P = const / V.
This means that the graph of the isothermal process in an ideal gas will be a hyperbole curve. Three hyperbolas are shown in the figure below.
Each of them is called an isotherm. The higher the temperature in the system, the farther away from the coordinate axes the isotherm will be. From the figure above, we can conclude that green corresponds to the highest temperature in the system, and blue corresponds to the lowest, provided that the amount of substance in all three systems is the same. If all the isotherms in the figure are built for the same temperature, then this means that the green curve corresponds to the largest system in terms of the amount of substance.
Change in internal energy during an isothermal process
In ideal gas physics, internal energy is understood to mean kinetic energy associated with rotational and translational motion of molecules. From the kinetic theory, it is easy to obtain the following formula for the internal energy U:
U = z / 2 * n * R * T.
Where z is the number of degrees of free movement of molecules. It varies from 3 (monatomic gas) to 6 (polyatomic molecules).
In the case of the isothermal process, the temperature remains constant, which means that the only reason for the change in internal energy is the release or arrival of particles of matter in the system. Thus, in closed systems during an isothermal change in their state, internal energy is conserved.
Isobaric and isochoric processes
In addition to the Boyle-Mariotte law, there are two more basic gas laws that have also been discovered experimentally. They bear the names of the French Charles and Gay-Lussac. Mathematically they are written as follows:
V / T = const at P = const;
P / T = const at V = const.
Charles's law says that during the isobaric process (P = const) the volume linearly depends on the absolute temperature. The Gay-Lussac law indicates a linear relationship between pressure and absolute temperature during an isochoric transition (V = const).
From the above equations it follows that from the process of isothermal graphics, isobaric and isochoric transitions differ significantly. If the isotherm is in the form of a hyperbola, then the isobar and isochore are straight lines.
Isobaric-isothermal process
When considering gas laws, they sometimes forget that, in addition to the values of T, P and V, the value of n in the Clapeyron-Mendeleev law can also change. If we fix the pressure and temperature, then we get the equation of the isobaric-isothermal transition:
n / V = const at T = const, P = const.
A linear relationship between the amount of substance and the volume suggests that under identical conditions, different gases containing the same amount of substance occupy equal volumes. For example, under normal conditions (0 ° C, 1 atmosphere), the molar volume of any gas is 22.4 liters. The considered law is called the Avogadro principle. It underlies Dalton's law of ideal gas mixtures.