31.Absolute temperature. Kinetic energy of molecule

Thermodynamic temperature is often also called absolute temperature.

Thermodynamic temperature is the absolute measure of temperature and it is one of the principal parameters of thermodynamics.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, called absolute zero, the particle constituents of matter have minimal motion and can become no colder.

In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy.

The absolute temperature affects mainly large letters T and is measured in Kelvins.

The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy:

   where  is the Boltzmann constant, unless that degree of freedom is in the quantum regime.

The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container. Kinetic theory explains macroscopic properties of gases, such as pressure, temperature, viscosity, thermal conductivity, and volume, by considering their molecular composition and motion. The theory posits that gas pressure is due to the impacts, on the walls of a container, of molecules or atoms moving at different velocities.

32. Degrees of molecule freedom. The law of equipartition of energy.

The vast majority of physical systems can not be in one, and in many states, described as continuous (coordinates of the body) and discrete (quantum numbers of an electron in an atom) variables. Independent "direction", the variables that characterize the state of the system, called the degrees of freedom.

It is important to note that the number of degrees of freedom equal to the minimum number of variables required to fully describe the state of the system. For example, the position of the mathematical pendulum can be described as an angle of rotation around its axis and by two coordinates of a material point position relative to the axis. However, such a pendulum is only one degree of freedom, instead of two (as it may appear in the second case) since only one angle of rotation is sufficient to describe the position of the system at any given time.

The theorem of equipartition of energy states that molecules in thermal equilibrium have the same average energy associated with each independent degree of freedom of their motion.

The equipartition result serves well in the definition of kinetic temperature since that involves just the translational degrees of freedom, but it fails to predict the specific heats of polyatomic gases because the increase in internal energy associated with heating such gases adds energy to rotational and perhaps vibrational degrees of freedom. Each vibrational mode will get kT/2 for kinetic energy and kT/2 for potential energy - equality of kinetic and potential energy is addressed in the virial theorem. Equipartition of energy also has implication for electromagnetic radiation when it is in equilibrium with matter, each mode of radiation having kT of energy in the Rayleigh-Jeans law.