Thermodynamics is an independent branch of physics that studies the processes of transition between system states, while operating with macroscopic characteristics. One of the important objects of study of thermodynamics is the ideal gas. This article is devoted to the consideration of the ideal gas concept and the units of measurement of the universal gas constant.
Perfect gas
The gas aggregate state of matter is characterized by a random arrangement of particles, the distance between which is much larger than their size. These particles are in constant motion, so the gas does not retain its shape and its volume.
An ideal gas is any substance whose particle size and interactions between which can be neglected. In the framework of the ideal gas concept, it is believed that any collisions of particles with the walls of the vessel are absolutely elastic. The average kinetic energy of particles uniquely determines the temperature of an ideal gas.
Most real gases that are at not too high pressures and not too low temperatures can be considered ideal with high accuracy.
Universal equation of state
This is the name of the equation, which combines all the important thermodynamic parameters of an ideal gas system within the framework of one expression. We write it down:
P * V = n * R * T.
Here P and V are the pressure in pascals and the volume in cubic meters, n and T are the amount of substance in moles and the temperature of the system in Kelvin. This equality is also called the Clapeyron-Mendeleev equation or law in honor of the French physicist and engineer and Russian chemist of the 19th century, who derived this equation from experimental experience accumulated by previous generations of scientists.
The universal equation of state of the system allows you to get any gas law. For example, the Gay-Lussac law follows directly from it if the volume is set constant during the thermodynamic process.
We have decoded 4 of the 5 notations present in the formula above. The fifth is the coefficient R. It is called the universal gas constant. The SI unit of measure for it is the joule per mole-kelvin (J / (mol * K)). What is this value, we consider in more detail later in the article.
R constant in physics
Above, we saw that this is a certain coefficient of proportionality between pressure, volume, temperature and the amount of substance. The unit of measurement of the universal gas constant in the SI system is J / (mol * K). Its value with an accuracy of three decimal places is 8.314. This number means that one mole of ideal gas, when heated to 1 kelvin, will perform 8.314 joules during its expansion.
The constant R can also be interpreted in a slightly different way: if one expends an energy of 8.314 joules to heat one mole of gas, then its temperature will increase by 1 kelvin. In other words, R characterizes the relationship between energy and temperature for a fixed amount of substance.
Note that the value of R in physics is not a basic (fundamental) constant such as the speed of light or Planck's constant. Therefore, by choosing the appropriate temperature scale and the number of particles in the system, one can achieve that R will be equal to 1.
For the first time, D. I. Mendeleev introduced the constant R into physics, replacing it with a number of other constants in the universal equation of state of Clapeyron. Note that although the value of R is introduced for gases, in modern physics it is also used in the equations of Dulong and Petit, Clausius-Mossotti, Nernst, and some others.
Constants kB and R
People who are familiar with physics may have noticed that there is another constant, which in all physical equations acts as a conversion factor between energy and temperature. This quantity is called the Boltzmann constant (k B ). It is 1.38 * 10 -23 J / K. Obviously, there must be a mathematical relationship between k B and R. Such a relationship does exist, it has the following form:
R = k B * N A.
Here N A is a huge number called the Avogadro number. It is equal to 6.02 * 10 23 . If the number of particles in the system is N A , then they say that the system contains 1 mol of substance.
Thus, the Boltzmann constant and the universal gas constant, in fact, are one and the same conversion coefficient between temperature and energy with the only difference that k B is used for microscopic processes, and R - for macroscopic ones.
The solution of the problem
After getting acquainted with the units of measurement of the universal gas constant, it is proposed to obtain them from the universal equation for the ideal gas, which was given in the article. The figure below depicts this equation.
Express from it the value of R, we obtain:
R = P * V / (n * T).
Now we substitute the corresponding unit of measurement for each physical quantity and simplify the expression obtained:
[R] = [Pa * m 3 / (mol * K)] = [N / m 2 * m 3 / (mol * K)] = [N * m / (mol * K)] = [J / (mol *TO)].
As you can see, when obtaining units of measure for R, we simplified only the units of measure of the numerator. First, the formula for pressure was used, and then the product of units of force by units of distance was converted to units of work.