Сформулируйте вопросы на английском языке и дайте ответы на них. Что такое степень свободы? Сформулируйте теорему о равнораспределении энергии.
Degree of freedom
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, the position of a figure in the plane has three degrees of freedom: its orientation and the two coordinates of any fixed point of the figure.
In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that models the system is only implicitly defined.
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 and that the energy is
The equipartition result
Сформулируйте вопросы на английском языке и дайте ответы на них. Сформулируйте закон распределения Больцмана.
Specify The Boltzmann distribution law.
The Boltzmann distribution law says that if the energy associated with some
state or condition of a system is ε then the frequency with which that state or
condition occurs, or the probability of its occurrence, is proportional to
(1.1)
where T is the system’s absolute temperature and where k is the Boltzmann
constant, which the reader will already have encountered in the kinetic theory
of gases:
k = 1.38×10−23 J/K = 1.38×10−16 erg/K.
Сформулируйте вопросы на английском языке и дайте ответы на них. Что такое функции распределения Максвелла-Больцмана?
What is The Maxwell–Boltzmann distribution functions?
Maxwell's law gives the distribution of the particle kinetic energy , and Boltzmann's law - the distribution of particles on the values of the potential energy . Both distributions can be combined into a single law Maxwell – Boltzmann
Here n0 - number of molecules per unit volume at the point where U = 0 , E = U + K - total energy .
In the last expression , the potential and kinetic energy , and hence the total energy E , can take a continuous range of values. If the energy of the particle can take only a discrete set of values E1, E2, ..., ( as is the case , for example, the internal energy of the atom) , then the Boltzmann distribution has the form :
where Ni - the number of particles in a state with energy Ei, and A> - coefficient of proportionality , which must satisfy the condition
where N - total number of particles in the system.
Then
the final expression of the Maxwell distribution - Boltzmann case of
discrete energy values will be:
Сформулируйте вопросы на английском языке и дайте ответы на них. Что такое длина свободного пробега? Что такое тепловая машина?
What is the mean free path? What is a heat engine?
In physics, the mean free path is the average distance travelled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions),which modify its direction or energy or other particle properties.
The mean free path or average distance between collisions for a gas molecule may be estimated from kinetic theory. Serway's approach is a good visualization - if the molecules have diameter d, then the effective cross-section for collision can be modeled by
using a circle of diameter 2d to represent a molecule's effective collision area while treating the "target" molecules as point masses. In time t, the circle would sweep out the volume shown and the number of collisions can be estimated from the number of gas molecules that were in that volume.
A heat engine typically uses energy provided in the form of heat to do work and then exhausts the heat which cannot be used to do work. Thermodynamics is the study of the relationships between heat and work. The first law and second law of thermodynamics constrain the operation of a heat engine. The first law is the application of conservation of energy to the system, and the second sets limits on the possible efficiency of the machine and determines the direction of energy flow
Heat
engines are typically illustrated on a PV diagram