Сформулируйте вопросы на английском языке и дайте ответы на них. Сформулируйте предположения молекулярной модели идеального газа.
Describe the molecular model for an ideal gas
Ideal gas: A theoretical gas composed of randomly moving non-interacting particles. At normal conditions such as standard temperature and pressure, most real gases behave qualitatively like an ideal gas.
Kinetic model of an ideal gas: A model which treats a gas as many molecules subject to the following assumptions:
· The molecules obey Newton’s laws
· The intermolecular forces are negligible
· The molecules are spherical with negligible volume
· The motion of the molecules is random
· The collisions are perfectly elastic
· The time taken for a collision is negligible.
The
ideal gas equation is:
or
Universal
Gas Constant:
Сформулируйте вопросы на английском языке и дайте ответы на них. Как записывается связь между давлением и кинетической энергией газов?
Describe relationship between pressure and molecular kinetic energy.
Сформулируйте вопросы на английском языке и дайте ответы на них. Что такое степень свободы? Сформулируйте теорему о равнораспределении энергии.
What is the degree of freedom? Specify the energy equipartition theorem.
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:
