15-06-2012, 03:43 PM
entropy
[attachment=24601]
Traditional understanding of entropy
Clausius law of entropy
Boltzmann and Gibbs approach of statistical thermodynamics
Stannon entropy
Clausius law of entropy
Assumption 1 system cycle is going through two process isotherml and adiabatic.
What he found ?..
Assumption 2 equilibrium states are infinitely near than we can represent in the terms of exact differential.
Boltzmann and Gibbs approach of statistical thermodynamics
They calculated the probability of finding of N particle
when it is distributed in free space
When distinguishable particle cover the quantum state gi
Now the probability of free state and Probability covering the quantum state gi Are expressed in a single function.
By using “The principal of Caratheodory” they explained the existance of entropy
dQ=Adx+Bdy+Cdz ……(1)
dQ=Adx+Bdy+Cdz =TdS. ……….(2)
Stannon entropy
Stannon also the concept of statistical thermodynamics to describe the degree of freedom of the molecules in solid on the act of charge(electricity).
Dispersion set
Assuming that the heat ΔQ is small and that the speed at which it is transferred to the system is slow, in order to avoid significant perturbations of the system, Clausius defined the entropy variation of a material system to be:
Dispersion is energetically equivalent to the disordered element or to the degree of freedom of molecules.
Hence from the law of equipartition – mean energy is equal to the heat transferred by single element..
E =½KT
E directly proportional to temperature
Hence, T is inversely proportional to ΔN
EARTH SURFACE
Average temp. 300K
Dispersion cardinality ΔN1 = 4.83
ΔN1 / NA = 800 μmol
SUN PHOTOSPHERE
Average temp. 6000K
dispersion cardinality ΔN2 = 2.41
ΔN2/ NA = 40 μmol
SECOND PRINCIPAL
The second principle postulates that entropy cannot decrease in isolated systems. Any entropy increase that may possibly occur is then irreversible.
the heat engine achieves its maximum efficiency:
This can be transformed as follows
MY PROPOSAL…..
but actually in practice that high efficiency is not be not possible
system which affect the efficiency
Radiation system.
Thermal efficiency and derive efficiency.
Equipartition and quanta of the system
Radiation system
Mean quantum energy which is equal to 2.7KT
It means E=2.7KT
or, ΔQ = (2.7KT ). ΔN
therefore ΔS=(2.7K). ΔN
The above equation revels the assumption made the last slide…..
therefore above equation may be reduced as follow …
ΔS=(1/2K)(5.7).ΔN
ΔS=(1/2K).ΔN*
Now concept of effective cardinality is introduced.
Efficiency
Two type of efficiency is really affecting the system
Thermal efficiency : power of engine is derived by the help of the entropy gradient including thermal efficiency.
power of the engine is a quadratic function of its efficiency η.
efficiency of
Root 1 – zero
Root 2 - η max
[attachment=24601]
Traditional understanding of entropy
Clausius law of entropy
Boltzmann and Gibbs approach of statistical thermodynamics
Stannon entropy
Clausius law of entropy
Assumption 1 system cycle is going through two process isotherml and adiabatic.
What he found ?..
Assumption 2 equilibrium states are infinitely near than we can represent in the terms of exact differential.
Boltzmann and Gibbs approach of statistical thermodynamics
They calculated the probability of finding of N particle
when it is distributed in free space
When distinguishable particle cover the quantum state gi
Now the probability of free state and Probability covering the quantum state gi Are expressed in a single function.
By using “The principal of Caratheodory” they explained the existance of entropy
dQ=Adx+Bdy+Cdz ……(1)
dQ=Adx+Bdy+Cdz =TdS. ……….(2)
Stannon entropy
Stannon also the concept of statistical thermodynamics to describe the degree of freedom of the molecules in solid on the act of charge(electricity).
Dispersion set
Assuming that the heat ΔQ is small and that the speed at which it is transferred to the system is slow, in order to avoid significant perturbations of the system, Clausius defined the entropy variation of a material system to be:
Dispersion is energetically equivalent to the disordered element or to the degree of freedom of molecules.
Hence from the law of equipartition – mean energy is equal to the heat transferred by single element..
E =½KT
E directly proportional to temperature
Hence, T is inversely proportional to ΔN
EARTH SURFACE
Average temp. 300K
Dispersion cardinality ΔN1 = 4.83
ΔN1 / NA = 800 μmol
SUN PHOTOSPHERE
Average temp. 6000K
dispersion cardinality ΔN2 = 2.41
ΔN2/ NA = 40 μmol
SECOND PRINCIPAL
The second principle postulates that entropy cannot decrease in isolated systems. Any entropy increase that may possibly occur is then irreversible.
the heat engine achieves its maximum efficiency:
This can be transformed as follows
MY PROPOSAL…..
but actually in practice that high efficiency is not be not possible
system which affect the efficiency
Radiation system.
Thermal efficiency and derive efficiency.
Equipartition and quanta of the system
Radiation system
Mean quantum energy which is equal to 2.7KT
It means E=2.7KT
or, ΔQ = (2.7KT ). ΔN
therefore ΔS=(2.7K). ΔN
The above equation revels the assumption made the last slide…..
therefore above equation may be reduced as follow …
ΔS=(1/2K)(5.7).ΔN
ΔS=(1/2K).ΔN*
Now concept of effective cardinality is introduced.
Efficiency
Two type of efficiency is really affecting the system
Thermal efficiency : power of engine is derived by the help of the entropy gradient including thermal efficiency.
power of the engine is a quadratic function of its efficiency η.
efficiency of
Root 1 – zero
Root 2 - η max