The theory of skating
The increasing of pressure on the ice is decreased the melting temperature of ice. The nascent thin film of water decreases the friction appreciably!
,
where
- it is a difference between specific volume of water and ice.
where m – it is the mass of man;
S – it is the area of skate.
Calculate the minimal temperature for skating!
The pVT - diagram
The foundations of kinetics
The physical kinetics deals with the TD system near the equilibrium.
The local equilibrium.
The disequilibrium reduces to arising of substance flux, energy flux and momentum flux. There are so called transport phenomena.
The subject of investigation there are three transport phenomena:
diffusion;
viscosity;
heat transfer.
The flux of physical value through the area.
T
he
heterogeneity of the physical value is a course of the flux of this
value.
Diffusion
Diffusion – it is a mutual penetration of the different substances in there mixture.
T
he
experimental law:
- it is the
density of mass flux
;
D
– is the coefficient of diffusion
;
- it is the
gradient of the density.
and
.
Viscosity
Viscosity – it is the transport of momentum due to the chaotic thermal motion of the molecules.
T
he
experimental law (Newton's law):
- it is the
viscosity's tension
;
x
- it is a
viscosity
.
- it is kinematical viscosity.
,
and
Thermal conductivity
Thermal conductivity – it is the energy transfer due to the chaotic thermal motion of the molecules.
T
he
experimental law (Fourier's law):
- it is the
density of heat flux
;
- it is the
thermo conductivity
.
- it is the
gradient of the temperature.
and
.
The molecular mechanism of the transport phenomena in gases
The mean free path of the molecule
L
et
us introduce the effective
diameter
d
of molecule and effective
cross section
:
Put
is an mean
frequency of collisions
and
is an
mean
free path of the molecule:
- it is an
average relative velocity of the molecule;
n – it is a concentration of the molecules;
- it is the
volume of the tube with cross section
that molecule moves inside for one second.
; 
;
,
because
due to chaotic motions.
- it is a mean free path of molecule.
For ideal gas therefore:
The evaluation of mean free path:
;
We can fined the mean distance between the molecules l from the volume per one molecule:
;
; 
;
So 
.
The general transport equation
The density flux of molecules along x axis:
The property G may be energy, momentum, charge…
it is a general equation for transport phenomena.
Diffusion (self diffusion)
n – it is the concentration of marked particles;
-
it is the concentration of all
particles.
For oxygen
and nitrogen at normal conditions
Viscosity
The
viscosity of gases at normal conditions
Thermal conductivity
- it is a specific heat at constant volume
- it is a density.
The dependence of the coefficients of transfer on TD parameters
;
Vacuum
Knudsen's number:
- it is vacuum;
- it is a solid medium.
Dewar Flask
Thermodynamic relations and potentials
All calculations in thermodynamics are based on functions of state that called thermodynamic potentials. For any set of independent parameters there are own thermodynamic potential. The changing of the potentials at the process defines the work done by the system or the quantity of heat received by the system. Below we shall use the inequality:
The equality sign corresponds to the reversible processes, the inequality sign – to the irreversible. Thermodynamic potentials are the functions of state.
Let us consider an example for this calculation.
If
then
; 
If
then
; 
Thermal radiation.
The pressure of the photon gas:
;
;
- it is a density of energy radiation.
;
;
(
is
independent on volume);
;
;
- it is Stefan-Boltzmann law for radiation.