Thermal apparatuses
Thermal engine.
For ideal engine:
;
;
and
For real engine (diesel):
Heat pump.
Refrigerator:
COP (cooling mode):
For ideal refrigerator:
;
;
and
For real refrigerator:
Heat pump as a heater.
H eater:
COP (heating mode):
For ideal heater:
;
;
and
For real refrigerator:
The processes with minimum of the increasing of entropy – that is a real conservation of energy!
Entropy on a Microscopic Scale
The cause of the tendency of an isolated system toward disorder is easily explained. To do so, let’s distinguish between microstates and macrostates of a system.
A microstate is a particular configuration of the individual constituents of the system. For example, the description of the ordered velocity vectors of the air molecules in your room refers to a particular microstate, and the more likely haphazard motion is another microstate. A macrostate is a description of the system’s conditions from a macroscopic point of view. For a thermodynamic system, macrostates are described by macroscopic variables such as pressure, density, and temperature.
Macrostate {p, V, T, …}
Microstate {
,
}
The
probability to fined the molecule in the left part of volume is equal
to
.
The
probability of each microstate is
.
Where
- is a probability to fined molecule in the defined part of vessel (A
or B).
T
he
ways for macrostate The numbers The probability
of states of macrostate
The probability of macrostate is proportional to the numbers
of microstates that correspond to that macrostate.
Entropy
The
adiabatic expansion of the gas to vacuum from volume
to
.
In this process
,
,
,
.
Let us consider the isothermal reversible process.
From the probability theory.
The probability of the initial state is:
The probability of the final state is:
For numbers of states due to independence of events:
For entropy there is an addition law:
The entropy is a "measure of disorder" of the system.
The state of equilibrium is characterized by maximum of entropy.
Equilibrium and phase transformations of matter
The phase of matter – it is a physically homogeneous part of matter that separate from other parts by border (water, ice, vapor).
The phase equilibrium – it is the steady state of TD system that consists of various phases.
The phase transformation – it is a process with one phase transforms to another.
Phase transformations of first and secondary types.
The latent heat at phase transformations.
Molecular mechanism of evaporation.
Experimental isotherms of real gas
K: - it is a critical point for which:
and
.
CD – it is range of phase changes.
Isothermal phase change take place with pressure is constant.
Van der Waals isotherms
The range
A-B can not exist because
that is impossible.
C-A: it is overheated liquid;
B-D: it is overcooled vapor.
Wilson's camera, bubbled camera.
Diagram of states.
Critical parameters
From this system we have the critical parameters:
; 
; 
.
; 
; 
From last expression one can conclude that near critical point the numbers of structural elements of real gas are less then in ideal gas.
Nondimensional equation of state
Let us introduce new nondimensional variables:
; 
; 
.
So
It is universal equation for any real gas.
Phase transformations. The diagram of equilibrium
In the phase transformations of first type there is latent heat exists.
Latent heat of evaporation (condensation)
;latent heat of melting (crystallization)
;latent heat of sublimation (condensation)
.
Klapeiron's –Klausius's equation
- it is a
latent specific heat for phase transformation
from
phase 1 to phase 2;
and
- are the specific volumes (
)
of phase 1 and phase 2.
The diagram of equilibrium
Triple point: it is equilibrium for three phases.
Water:
; 
Carbon
dioxide
:
;
The
temperature of sublimation carbon dioxide
at normal pressure is
Examples.
The theory of pressure-cooker.
T
The increase of pressure reduces the increase of bowling temperature. And at high temperature the cooking time is decreased.
It is difficult to cook quickly the potato on mountains!
Artificial ice (solid ).
Phase transformation from solid to gas at normal pressure occurs without liquid phase.