Gas is the highest energy state of a substance. In physics, this state of aggregation is studied on the basis of a simplified model called the ideal gas. In this article, we consider in detail the basic law for this model - the Clapeyron-Mendeleev law.
What is the physical essence of the model?
Every student knows that gases easily take on the arbitrary shape of the vessel in which they are located. They are also easy to compress and expand. Despite these properties, in them the molecules and atoms still interact with each other with the help of weak Van der Waals forces. If these forces are not taken into account when performing calculations, but it is assumed that all the energy of the system is the kinetic energy of moving, rotating and oscillating molecules, then we will get an ideal gas.
To the noted approximation, one should also add the approximation of the dimensionlessness of molecules. The validity of this statement is obvious if we recall that at not too high pressures and not too low temperatures, the molecules and atoms of the systems under study are at great distances from each other.
Thus, the considered model assumes the presence in the system of material non-interacting points that randomly move in all directions. Their average kinetic energy determines the temperature of the system, and constant elastic collisions with the walls of the vessel determine the presence of pressure.
Brief historical background
Scientists began to study the properties and behavior of gases with the advent of the New Time. At the end of the 17th century, Boyle and Marriott independently discovered experimentally the law describing the isothermal process in the system. After this, Charles and Gay-Lussac discovered the laws for isobaric and isochoric processes at the beginning of the 19th century. Finally, Avogadro, studying the isobaric-isothermal process in chemically different systems, formulated the principle that bears his name.
All of these prerequisites created favorable conditions for Emil Clapeyron to write down an equation in 1834 linking the three main thermodynamic parameters into a single equality. The Clapeyron equation was somewhat inconvenient for practical use due to the large number of constants in it.
In 1874, D. I. Mendeleev introduced the universal gas constant R into it. For this reason, it is customary to call the modern form of the universal gas law the Clapeyron – Mendeleev formula.
Type of universal formula
We present the Clapeyron-Mendeleev equation with an explanation of the values of its variables and the relationship between them. The formula is written like this:
P * V = n * R * T.
Here, from left to right are the values of pressure, volume, amount of substance, gas constant and absolute temperature.
The universal equation indicates that the product of volume in cubic meters by the pressure in pascals in the system should be proportional to the product of the absolute temperature in kelvins and the amount of substance in moles. The constant R shows the work done by 1 mole of gas during isobaric expansion when it is heated by 1 K. This work is 8.314 J.
The Clapeyron-Mendeleev equation is called universal because it does not depend on the chemical characteristics of the system under study, and that any gas law can be obtained from it by imposing appropriate mathematical conditions.