Each person in the course of his life collides with bodies that are in one of the three aggregate states of matter. The simplest state to study is the gas state. In the article, we consider the concept of an ideal gas, give the equation of state of the system, and also pay some attention to the description of the absolute temperature.
The gas state of the substance
Each student is well aware of the state of matter in question when he hears the word "gas". This word means a body that can occupy any volume provided to it. It is not able to maintain shape, because it can not resist even the most insignificant external influences. Also, gas does not preserve volume either, which distinguishes it not only from solids, but also from liquids.
Like liquid, gas is a fluid substance. In the process of movement of solids in gases, the latter impede this movement. The emerging force is called resistance. Its value depends on the speed of the body in the gas.
Vivid examples of gases are air, natural gas, which is used for heating homes and cooking, inert gases (Ne, Ar), which fill the advertising tubes of a glow discharge, or which are used to create an inert (non-aggressive, protective) environment during welding.
Perfect gas
Before proceeding to the description of gas laws and equations of state, one should well understand the question of what an ideal gas is. This concept is introduced in molecular kinetic theory (MKT). Any gas that satisfies the following characteristics is called ideal:
- The particles forming it do not interact with each other except for direct mechanical collisions.
- As a result of the collision of particles with the walls of the vessel or between themselves, their kinetic energy and momentum are preserved, that is, the collision is considered absolutely elastic.
- Particles do not have dimensions, but have finite mass, that is, they are similar to material points.
Naturally, any gas is not ideal, but real. Nevertheless, to solve many practical problems, the indicated approximations are quite valid and can be used. There is a general rule of thumb, which states: regardless of the chemical nature, if a gas has a temperature above room temperature and a pressure of the order of atmospheric pressure or lower, then it can be considered ideal with high accuracy and the equation of state of an ideal gas can be used to describe it.
Clapeyron-Mendeleev Law
Transitions between different aggregate states of matter and processes within the framework of one aggregate state are involved in thermodynamics. Pressure, temperature and volume are three quantities that uniquely determine any state of a thermodynamic system. The formula of the equation of state of an ideal gas combines all three of these quantities into a single equality. We write this formula:
P * V = n * R * T
Here P, V, T are pressure, volume, temperature, respectively. The value n is the amount of substance in moles, and the symbol R denotes the universal constant of gases. This equality shows that the greater the product of pressure and volume, the greater should be the product of the amount of substance and temperature.
The formula for the gas equation of state is called the Clapeyron-Mendeleev law. In 1834, the French scientist Emile Clapeyron, generalizing the experimental results of his predecessors, came to this equation. However, Clapeyron used a number of constants, which Mendeleev subsequently replaced with one - the universal gas constant R (8.314 J / (mol * K)). Therefore, in modern physics, this equation is named after the names of French and Russian scientists.
Other forms of equation writing
Above, we wrote down the equation of state of an ideal Mendeleev-Clapeyron gas in a generally accepted and convenient form. However, in problems in thermodynamics, a slightly different kind may often be required. Below are three more formulas that directly follow from the written equation:
P * V = N * k B * T;
P * V = m / M * R * T;
P = Ο * R * T / M.
These three equations are also universal for an ideal gas, only such quantities as mass m, molar mass M, density Ο and the number of particles N that make up the system appear in them. The symbol k B here denotes the Boltzmann constant (1.38 * 10 -23 J / K).
Boyle-Marriott Law
When Clapeyron drafted his equation, he was based on gas laws that had been discovered experimentally several decades earlier. One of them is the Boyle-Marriott law. It reflects an isothermal process in a closed system, as a result of which macroscopic parameters such as pressure and volume change. If we put T and n constant in the equation of state of an ideal gas, the gas law then takes the form:
P 1 * V 1 = P 2 * V 2
This is the Boyle-Mariotte law, which says that the product of pressure on volume is maintained during an arbitrary isothermal process. In this case, the values ββof P and V themselves change.
If we plot the dependence P (V) or V (P), then the isotherms will be hyperbolas.
The laws of Charles and Gay-Lussac
These laws mathematically describe isobaric and isochoric processes, that is, such transitions between states of a gas system in which pressure and volume are retained, respectively. Charles's law can be mathematically written as follows:
V / T = const for n, P = const.
The Gay-Lussac Law is written as follows:
P / T = const for n, V = const.
If both equalities are presented in the form of a graph, then we get straight lines that are inclined at some angle to the abscissa axis. This type of graph indicates a direct proportionality between volume and temperature at constant pressure and between pressure and temperature at constant volume.
Note that all three gas laws considered do not take into account the chemical composition of the gas, as well as the change in its amount of substance.
Absolute temperature
In everyday life, we are used to using the Celsius temperature scale, since it is convenient for describing the processes surrounding us. So, water boils at a temperature of 100 o C, and freezes at 0 o C. In physics, this scale is inconvenient, therefore, the so-called absolute temperature scale, which was introduced by Lord Kelvin in the middle of the XIX century, is used. According to this scale, temperature is measured in Kelvin (K).
It is believed that at a temperature of -273.15 o C there are no thermal vibrations of atoms and molecules, their translational motion is completely stopped. This temperature in degrees Celsius corresponds to an absolute zero in Kelvin (0 K). The physical meaning of absolute temperature follows from this definition: it is a measure of the kinetic energy of particles that make up matter, for example, atoms or molecules.
In addition to the physical meaning of absolute temperature given above, there are other approaches to understanding this quantity. One of them is the mentioned gas law of Charles. We write it in the following form:
V 1 / T 1 = V 2 / T 2 =>
V 1 / V 2 = T 1 / T 2 .
The last equality means that at a certain amount of substance in the system (for example, 1 mol) and a certain pressure (for example, 1 Pa), the gas volume uniquely determines the absolute temperature. In other words, an increase in gas volume under these conditions is possible only due to an increase in temperature, and a decrease in volume indicates a decrease in T.
Recall that, in contrast to the temperature on the Celsius scale, the absolute temperature cannot take negative values.
Avogadro principle and gas mixtures
In addition to the gas laws set forth above , the equation of state for ideal gas also leads to the principle discovered by Amedeo Avogadro at the beginning of the 19th century, which bears his last name. This principle establishes that the volume of any gas at constant pressure and temperature is determined by the amount of substance in the system. The corresponding formula looks like this:
n / V = ββconst at P, T = const.
The written expression leads to the Dalton law for gas mixtures known in ideal gas physics. This law states that the partial pressure of a gas in a mixture is uniquely determined by its atomic fraction.
Problem solving example
In a closed vessel with rigid walls containing ideal gas, the pressure increased by 3 times as a result of heating. It is necessary to determine the final temperature of the system, if its initial value was equal to 25 o C.
First, we convert the temperature from degrees Celsius to Kelvin, we have:
T = 25 + 273.15 = 298.15 K.
Since the walls of the vessel are rigid, the heating process can be considered isochoric. For this case, we apply the Gay-Lussac law, we have:
P 1 / T 1 = P 2 / T 2 =>
T 2 = P 2 / P 1 * T 1 .
Thus, the final temperature is determined from the product of the ratio of the pressures and the initial temperature. Substituting the data into the equality, we get the answer: T 2 = 894.45 K. This temperature corresponds to 621.3 o C.