The study of the properties of an ideal gas is an important topic in physics. Acquaintance with the characteristics of gas systems begins with a consideration of the Boyle-Mariotte equation, since it is the first experimentally discovered law of ideal gas. Consider it in more detail in the article.
What is meant by ideal gas?
Before talking about the Boyle-Mariotte law and the equation that describes it, we define the ideal gas. It is customary to mean a fluid substance in which its constituent particles do not interact with each other, and their sizes are negligibly small in comparison with the average interparticle distances.
In fact, any gas is real, that is, the atoms and molecules that make it up are of a certain size and do not interact with each other with the help of Van der Waals forces. However, at high absolute temperatures (more than 300 K) and low pressures (less than one atmosphere), the kinetic energy of atoms and molecules is much higher than the energy of Van der Waals interactions, therefore, a real gas under these conditions can be considered ideal with high accuracy.
Boyle-Marriott equation
European scientists actively studied the properties of gases during the 17th-19th centuries. The very first gas law that was discovered experimentally was the law describing the isothermal processes of expansion and contraction of a gas system. The corresponding experiments were conducted by Robert Boyle in 1662 and Edm Mariott in 1676. Each of these scientists independently showed that during an isothermal process in a closed gas system, pressure changes to volume inversely. The experimentally obtained mathematical expression of the process is written as follows:
P * V = k
Where P and V is the pressure in the system and its volume, k is a certain constant, the value of which depends on the amount of gas substance and its temperature. If we plot the dependence of the function P (V) on the graph, then it will be a hyperbola. An example of these curves is shown below.
The written equality is called the Boyle-Marriott equation (law). This law can be briefly formulated as follows: the expansion of an ideal gas at a constant temperature leads to a proportional decrease in the pressure in it; on the contrary, the isothermal compression of the gas system is accompanied by a proportional increase in pressure in it.
The ideal gas equation
Boyle-Mariotte law is a special case of a more general law, which bears the names of Mendeleev and Clapeyron. Emil Clapeyron, summarizing the experimental information on the behavior of gases under various external conditions, in 1834 received the following equation:
P * V = n * R * T
In other words, the product of the volume V of the gas system by the pressure P in it is directly proportional to the product of the absolute temperature T by the amount of substance n. The coefficient of this proportionality is denoted by the letter R and is called the gas universal constant. In the written equation, the value of R appeared due to the replacement of a number of constants, which was made by Dmitry Ivanovich Mendeleev in 1874.
It is easy to see from the universal equation of state that the constancy of the temperature and quantity of the substance guarantees the invariability of the right side of the equality, which means that the left side of the equality will also remain constant. In this case, we obtain the Boyle-Mariotte equation.
Other gas laws
The equation written in the Clapeyron-Mendeleev paragraph above contains three thermodynamic parameters: P, V, and T. If each of them is fixed and the other two are allowed to change, then we obtain the Boyle-Marriott, Charles, and Gay-Lussac equations. The Charles law speaks of direct proportionality between volume and temperature for the isobaric process, while the Gay-Lussac law states that in the case of an isochoric transition, the gas pressure increases or decreases in absolute temperature in direct proportion. The corresponding equations are as follows:
V / T = const at P = const;
P / T = const at V = const.
Thus, the Boyle-Mariotte law is one of the three main gas laws. Nevertheless, it differs from the others in terms of graphic dependence: the functions V (T) and P (T) are straight lines, the function P (V) is a hyperbole.
Example of the task of applying the Boyle-Marriott law
The volume of gas in the cylinder under the piston in the initial position was 2 liters, and its pressure was 1 atmosphere. What became the gas pressure after the piston rose and the volume of the gas system increased by 0.5 liters. The process is considered isothermal.
Since we are given the pressure and volume of an ideal gas, and it is also known that the temperature during its expansion remains unchanged, we are entitled to use the Boyle-Mariotte equation in the following form:
P 1 * V 1 = P 2 * V 2
This equality means that the product by the pressure volume is constant for each state of the gas at a given temperature. Expressing from the equation the value of P 2 , we obtain the final formula:
P 2 = P 1 * V 1 / V 2
When performing pressure calculations, you can use off-system units in this case, since the liters will decrease and we will get the pressure P 2 in the atmospheres. Substituting the data from the condition, we come to the answer to the question of the problem: P 2 = 0.8 atmosphere.