The thermodynamics of the gaseous state of aggregation of matter is an important branch of physics that studies the thermodynamic equilibrium and quasistatic transitions in systems. The main model on which predictions of system behavior are based is the ideal gas model. Using it, the Mendeleev-Clapeyron equation was obtained. Let's consider it in the article.
Perfect gas
As you know, all real gases consist of molecules or atoms, the distances between which are too large compared to their sizes at low pressures. In addition, at high temperatures on the absolute scale, the kinetic energy of molecules exceeds their potential energy associated with weak dipole-dipole interactions (if in addition to these interactions there are other types of chemical bonds, for example, ionic or hydrogen, they make a significant contribution to the potential component of the internal system energy).
In this connection, for many real gases under conditions close to normal, their internal interactions and particle sizes can be neglected. These two main approximations make up the ideal gas model.
Mendeleev equation in physics
It is more correct and fair to call this equation the Clapeyron-Mendeleev law. The fact is that the French engineer Emile Clapeyron first recorded it in 1834. He did this by analyzing the gas laws of Boyle-Mariotte, Gay-Lussac and Charles, discovered by the beginning of the 19th century.
The merit of the domestic chemist Dmitry Mendeleev is that he gave the equation a modern and easy-to-use mathematical form. In particular, Mendeleev introduced into the equation a constant for all gases R = 8.314 J / (mol * K). Clapeyron himself used a number of empirical constants that impeded the computational process.
The Mendeleev-Clapeyron equation is written as follows:
P * V = n * R * T.
This equality means that the product of pressure P by the volume V in the left side of the expression is always proportional to the product of the absolute temperature T by the amount of substance n in the left side.
The expression under study allows one to obtain any gas law if two of its four parameters are fixed. In the case of isoprocesses, closed systems are investigated in which there is no exchange of matter with the environment (n = const). These processes are characterized by a single fixed thermodynamic parameter (T, P or V).
Task example
We now solve the problem of the Mendeleev-Clapeyron equation. It is known that oxygen weighing 500 grams is in a cylinder of 100 liters under a pressure of 2 atmospheres. What is the temperature in the cylinder, given that the system is in thermodynamic equilibrium.
Recall that, by definition, the amount of substance is calculated by the formula:
n = m / M.
Where m is the mass of all particles in the system, M is their average molar mass. This equality allows us to rewrite the Mendeleev equation in this form:
P * V = m * R * T / M.
Where do we get the working formula for this task:
T = P * V * M / (m * R).
It remains to translate all the quantities into SI units and substitute them into this expression:
T = 2 * 101325 * 0.1 * 0.032 / (0.5 * 8.314) = 156 K.
The calculated temperature is -117 o C. Although oxygen at this temperature is still gaseous (it condenses at -182.96 o C), under such conditions, the ideal gas model can only be used to obtain a qualitative estimate of the calculated value.