The main subject of studying the thermodynamics of gas systems is the change in thermodynamic states. As a result of such changes, the gas can do work and store internal energy. Let us study in the article below different thermodynamic transitions in an ideal gas. Particular attention will be paid to studying the graph of the isothermal process.
Ideal gases
Judging by the very name, we can say that 100% ideal gases do not exist in nature. However, many real substances satisfy this concept with practical accuracy.
An ideal gas is any gas in which interactions between its particles and their sizes can be neglected. Both conditions are satisfied only if the kinetic energy of the molecules will be much greater than the potential energy of the bonds between them, and the distances between the molecules will be much greater than the particle size.
To determine which isIf the gas under study is ideal, you can use a simple rule of thumb: if the temperature in the system is above room temperature, the pressure is not very different from atmospheric pressure or less than it, 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. A few decades later, it was brought by the Russian chemist Mendeleev to its modern form. This equation looks like this:
PV=nRT.
On the left side of the equation is the product of pressure P and volume V, on the right side of the equation is the product of temperature T and the amount of substance n. R is the 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 base. With the development of modern physics and the kinetic theory of fluids, the ideal gas equation can be derived from considering the microscopic behavior of the particles of the system.
Isothermal process
Regardless of whether this process occurs in gases, liquids or solids, it has a very clear definition. An isothermal transition is a transition between two states in which the temperature of the systempreserved, 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 an 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 17th century). It can be obtained by every student 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 get:
nRT=const=>
PV=const.
The last equality is the Boyle-Mariotte law. In physics textbooks, you can also find this form of writing it:
P1 V1=P2 V 2.
During the transition from isothermal state 1 to thermodynamic state 2, the product of volume and pressure remains constant for a closed gas system.
The studied law speaks of inverse proportionality between the values of P and V:
P=const / V.
This means that the graph of the isothermal process in an ideal gas will be a hyperbola 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 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 to the lowest, provided that the amount of substance in all threesystems 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 the physics of ideal gases, internal energy is understood as kinetic energy associated with the 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 / 2nRT.
Where z is the number of degrees of free movement of molecules. It ranges from 3 (monatomic gas) to 6 (polyatomic molecules).
In the case of an isothermal process, the temperature remains constant, which means that the only reason for the change in internal energy is the exit or arrival of particles of matter into the system. Thus, in closed systems, during an isothermal change in their state, internal energy is conserved.
Isobaric and isochoric processes
Besides the Boyle-Mariotte law, there are two more basic gas laws that were also discovered experimentally. They bear the names of the French Charles and Gay-Lussac. Mathematically, they are written like this:
V / T=const when P=const;
P / T=const when V=const.
Charles' law says that during an isobaric process (P=const) the volume depends linearly on the absolute temperature. Gay-Lussac's law indicates a linear relationship between pressure and absolute temperature at isochorictransition (V=const).
From the given equalities it follows that the graphs of isobaric and isochoric transitions differ significantly from the isothermal process. If the isotherm has the shape of a hyperbola, then the isobar and isochore are straight lines.
Isobaric-isothermal process
When considering the gas laws, it is sometimes forgotten 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 when T=const, P=const.
The linear relationship between the amount of substance and volume suggests that under the same conditions, different gases containing the same amount of substance occupy equal volumes. For example, under normal conditions (0 oC, 1 atmosphere), the molar volume of any gas is 22.4 liters. The considered law is called Avogadro's principle. It underlies D alton's law of ideal gas mixtures.
