The processes of compression, expansion, heating and cooling of gaseous systems play an important role in technology and nature, so understanding the laws that describe the transitions from one thermodynamic state to another is fundamental. It is most convenient to study and use these laws in graphical form. In this article, we consider the graphs of isoprocesses in physics.
What is meant by isoprocesses in gases?
When it is said that the closed system being studied has passed from the thermodynamic state 1 to state 2 as a result of a certain isoprocess, then we mean its quasistatic transition with a certain fixed thermodynamic parameter. A transition is called quasistatic because during its implementation the system deviates slightly from the equilibrium state, that is, the process itself is slow. In this case, the microscopic characteristics have time to level out over the entire volume, which allows one to determine macroscopic parameters at any time (pressure P, volume V, temperature T).
Below we will consider the three most important isoprocesses and the graphs that correspond to them.
Isoprocess at constant absolute temperature
It is also called isothermal. Mathematically, it is described by the Boyle-Mariotte law:
P * V = const.
Where the value of the constant depends on the amount of substance in the system and on its temperature.
If we construct a graph for this isoprocess in PV coordinates, then we get the hyperbola shown below, which approaches the axes of pressure and volume.
As you can see, each volume corresponds to one single pressure in the studied system. If you start to increase or decrease the temperature, then the isotherm will move away from the axes or approach them. In the graph below, the system with the highest temperature corresponds to a green hyperbole.
In some cases, it is convenient to represent the isotherm in the coordinate axes P-1 / V. Convenience is that the chart will represent a straight line.
Constant pressure isoprocess
It is called the isobaric transition. In practice, it is easy to obtain if any gas is heated in a cylinder with a movable piston. As a result of heating, the system increases its volume and temperature, keeping the pressure unchanged.
The formula for the isobaric process is called Charles's law and is as follows:
V / T = const.
The constant on the right side of the equation is uniquely determined if the number of molecules or atoms in the system and pressure are known.
Charles's law establishes a direct proportionality between temperature and volume with a positive angle of inclination; therefore, for the studied isoprocess, the graph is a straight line. An arbitrary isobar is shown below as an example.
Constant volume heating and cooling
The process indicated in the title of this paragraph is isochoric. The volume in this case is fixed, only pressure and temperature change. Changes to these values are calculated using the following expression:
P / T = const.
The constant const depends on the volume of the system and the amount of substance in it. The expression is called the Gay-Lussac Act. The corresponding graph in the PT axes represents an increasing linear dependence (see the main photo). An increase in the volume of the system while maintaining the number of particles in it leads to an approach to the isochore temperature axis.
The formulas and graphs of isoprocesses given in the article are valid only if the system under study is described with good accuracy by the ideal gas model. If this is not the case, then the graphical dependencies presented will be distorted, and they should be rebuilt using the van der Waals model for real gases.