When studying the gas state of matter in modern physics, a relatively simple model is used. It is based on the principles of molecular kinetic theory, proposed in the middle of the XVIII century by Daniel Bernoulli. In the framework of this model, the behavior of systems during various transformations is investigated. In this article, we present the formula of the Boyle-Mariotte law and the name of the isoprocess to which it is applicable.
Ideal gas model
It is based on a theory that considers molecules and atoms as material points moving in all directions at the same speed. The kinetic energy of the particles of the system determines the presence of temperature in it, and their constant collisions with the walls of the vessel lead to pressure. It is believed that in an ideal gas model the particles of the system do not interact with each other, that is, their potential energy is zero.
The behavior of any real gas is well described by this theory only if it is formed by chemically inert molecules or atoms, its pressure is low, and the temperature is within room temperature or exceeds it.
Boyle-Marriott Law: Formula and Formulation
In the second half of the 17th century, the Frenchman Edm Mariotte and the Englishman Robert Boyle independently established the following relationship between pressure P and volume V of the gas system:
P * V = const.
This equality was fulfilled with high accuracy for all studied gases only if the temperature t was kept constant. In physics, such a process is called isothermal. The corresponding graph for it will be the isotherm P (V).
From the formula of the Boyle-Mariotte law it follows that with an isothermal change of one equilibrium state to another, the pressure in the system increases (decreases) exactly as many times as its volume decreases (increases).
Although the law in question was obtained experimentally, at present it can be easily derived from the equation of state of an ideal gas (Clapeyron-Mendeleev law), which has the form:
P * V = n * R * t.
If we consider a closed system (the amount of substance n = const), then during the isothermal process in it (t = const) the right side of the equation will not change, which means that the left side will also remain constant, that is, we come to the formula of the Boyle-Marriott law . The value of R here is a universal gas constant.
An example of a schedule corresponding to the law in question is given above. The curve P (V) is called an isotherm and represents a hyperbola.
Task example
We show how to use the formula of the Boyle-Mariotte law to solve problems.
It is known that as a result of the isothermal process, the pressure in the system with an ideal gas decreased from 10 5 Pa to 10 4 Pa. How much has its volume changed, if at the beginning of the process it was equal to 10 liters.
We write the law of isothermal expansion of the gas in the following form:
P 1 * V 1 = P 2 * V 2 .
From here we can express the value of volume V 2 and calculate it:
V 2 = P 1 * V 1 / P 2 ;
V 2 = 10 5/10 4 * 10 = 100 liters.
Note that when calculating the volume, we did not translate the data into the SI system, since the pressure units were reduced. It remains to find the difference between the final and initial volume in order to get an answer to the question of the problem: V 2 - V 1 = 90 liters.