Entropy is a measure of the dispersal of energy in a system as a function of temperature. It is related to the number of microscopic configurations or "microstates" that are consistent with the macroscopic properties of the system. The more possible microstates there are, the higher the entropy. According to the second law of thermodynamics, isolated systems spontaneously evolve towards configurations with higher probability and maximum entropy.
Information theory and statistical mechanicsChandanShah35
Focused on basic terminology used in Statistical Mechanics, Relation ship between Information Theory and Statistical Mechanics and few terms related to quantum mechanics
Nuclear Decay - A Mathematical PerspectiveErik Faust
Radioactivity as a phenomenon is often misunderstood: if one says ‘Radioactive’, most people will think about disastrous electrical plants, dangerous bombs and other forms of life-threatening details. In my native Germany, members of the Green party have been campaigning for a decade to put an end to nuclear energy. Only few think of the useful aspects of this unique actuality, although radiotherapy is most promising of tools in the fight against cancer, and radioactive dating allows us to identify the age of any historical item. But even fewer people see radioactivity as the natural process that it actually is: A spontaneous mechanism, in which one nucleus decays into another. As an aspiring Physicist and Engineer, Radioactivity is one my favourite topics in the realm of science. I am fascinated at how we are able to predict exactly how many Nuclei will decay in a certain amount of time, but not say for certain which Nuclei exactly will do so.
Information theory and statistical mechanicsChandanShah35
Focused on basic terminology used in Statistical Mechanics, Relation ship between Information Theory and Statistical Mechanics and few terms related to quantum mechanics
Nuclear Decay - A Mathematical PerspectiveErik Faust
Radioactivity as a phenomenon is often misunderstood: if one says ‘Radioactive’, most people will think about disastrous electrical plants, dangerous bombs and other forms of life-threatening details. In my native Germany, members of the Green party have been campaigning for a decade to put an end to nuclear energy. Only few think of the useful aspects of this unique actuality, although radiotherapy is most promising of tools in the fight against cancer, and radioactive dating allows us to identify the age of any historical item. But even fewer people see radioactivity as the natural process that it actually is: A spontaneous mechanism, in which one nucleus decays into another. As an aspiring Physicist and Engineer, Radioactivity is one my favourite topics in the realm of science. I am fascinated at how we are able to predict exactly how many Nuclei will decay in a certain amount of time, but not say for certain which Nuclei exactly will do so.
Measurement
of
the
angle
θ
For
better
understanding
I
am
showing
you
a
different
particle
track
diagram
bellow.
Where
at
point
C
particle
𝜋! 𝑎𝑛𝑑 Σ!
are
created
and
the
Σ!
decays
into
𝜋∓ 𝑎𝑛𝑑 K!
particles
The
angle
θ
between
the
π−
and
Σ−
momentum
vectors
can
be
determined
by
drawing
tangents
to
the
π−
and
Σ−
tracks
at
the
point
of
the
Σ−
decay.
We
can
then
measure
the
angle
between
the
tangents
using
a
protractor.
Alternative
method
which
does
not
require
a
protractor
is
also
possible.
Let
AC
and
BC
be
the
tangents
to
the
π−
and
Σ−
tracks
respectively.
Drop
a
perpendicular
(AB)
and
measure
the
distances
AB
and
BC.
The
ratio
AB/BC
gives
the
tangent
of
the
angle180◦−θ.
It
should
be
noted
that
only
some
of
the
time
will
the
angle
θ
exceed
90◦
as
shown
here.
Determining
the
uncertainty
of
Measurements
In
part
B,
It
is
asked
to
estimate
the
uncertainty
of
your
measurements
of
𝜃
and
r.
Uncertainty
of
measurement
is
the
doubt
that
exists
about
the
result
of
any
measurement.
You
might
think
that
well-‐made
rulers,
clocks
and
thermometers
should
be
trustworthy,
and
give
the
right
answers.
But
for
every
measurement
-‐
even
the
most
careful
-‐
there
is
always
a
margin
of
doubt.
It
is
important
not
to
confuse
the
terms
‘error’
and
‘uncertainty’.
Error
is
the
difference
between
the
measured
value
and
the
‘true
value’
of
the
thing
being
measured.
Uncertainty
is
a
quantification
of
the
doubt
about
the
measurement
result
Since
there
is
always
a
margin
of
doubt
about
any
measurement,
we
need
to
ask
‘How
big
is
the
margin?’
and
‘How
bad
is
the
doubt?’
Thus,
two
numbers
are
really
needed
in
order
to
quantify
an
uncertainty.
One
is
the
width
of
the
margin,
or
interval.
The
other
is
a
confidence
level,
and
states
how
sure
we
are
that
the
‘true
value’
is
within
that
margin.
You
can
increase
the
amount
of
information
you
get
from
your
measurements
by
taking
a
number
of
readings
and
carrying
out
Quantum computing is the computing which uses the laws of quantum mechanics to process information. Quantum computer works on qubits, which stands for "Quantum Bits".
With quantum computers, factoring of prime numbers are possible.
Fi ck law
Diffusion: random walk of an ensemble of particles from region of high “concentration” to region of small “concentration”.
Flow is proportional to the negative gradient of the “concentration”.
Measurement
of
the
angle
θ
For
better
understanding
I
am
showing
you
a
different
particle
track
diagram
bellow.
Where
at
point
C
particle
𝜋! 𝑎𝑛𝑑 Σ!
are
created
and
the
Σ!
decays
into
𝜋∓ 𝑎𝑛𝑑 K!
particles
The
angle
θ
between
the
π−
and
Σ−
momentum
vectors
can
be
determined
by
drawing
tangents
to
the
π−
and
Σ−
tracks
at
the
point
of
the
Σ−
decay.
We
can
then
measure
the
angle
between
the
tangents
using
a
protractor.
Alternative
method
which
does
not
require
a
protractor
is
also
possible.
Let
AC
and
BC
be
the
tangents
to
the
π−
and
Σ−
tracks
respectively.
Drop
a
perpendicular
(AB)
and
measure
the
distances
AB
and
BC.
The
ratio
AB/BC
gives
the
tangent
of
the
angle180◦−θ.
It
should
be
noted
that
only
some
of
the
time
will
the
angle
θ
exceed
90◦
as
shown
here.
Determining
the
uncertainty
of
Measurements
In
part
B,
It
is
asked
to
estimate
the
uncertainty
of
your
measurements
of
𝜃
and
r.
Uncertainty
of
measurement
is
the
doubt
that
exists
about
the
result
of
any
measurement.
You
might
think
that
well-‐made
rulers,
clocks
and
thermometers
should
be
trustworthy,
and
give
the
right
answers.
But
for
every
measurement
-‐
even
the
most
careful
-‐
there
is
always
a
margin
of
doubt.
It
is
important
not
to
confuse
the
terms
‘error’
and
‘uncertainty’.
Error
is
the
difference
between
the
measured
value
and
the
‘true
value’
of
the
thing
being
measured.
Uncertainty
is
a
quantification
of
the
doubt
about
the
measurement
result
Since
there
is
always
a
margin
of
doubt
about
any
measurement,
we
need
to
ask
‘How
big
is
the
margin?’
and
‘How
bad
is
the
doubt?’
Thus,
two
numbers
are
really
needed
in
order
to
quantify
an
uncertainty.
One
is
the
width
of
the
margin,
or
interval.
The
other
is
a
confidence
level,
and
states
how
sure
we
are
that
the
‘true
value’
is
within
that
margin.
You
can
increase
the
amount
of
information
you
get
from
your
measurements
by
taking
a
number
of
readings
and
carrying
out
Quantum computing is the computing which uses the laws of quantum mechanics to process information. Quantum computer works on qubits, which stands for "Quantum Bits".
With quantum computers, factoring of prime numbers are possible.
Fi ck law
Diffusion: random walk of an ensemble of particles from region of high “concentration” to region of small “concentration”.
Flow is proportional to the negative gradient of the “concentration”.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
1. Entropy (S): a measure of the dispersal of energy,
as a function of temperature, in a system.
To understand entropy, we need to consider probability.
Think about a deck of cards…
2. Only one way to be ordered
in sequence like a new deck.
Many ways to be out of
sequence.
Improbable after shuffling
Random order much more
probable after shuffling
3. Spontaneous process: The gas atoms expand to occupy both
flasks when the valve is opened.
How is probability involved in this process?
Why??
Let’s do an exercise involving dice to understand
more about probability.
Note: probability is the likelihood of an event occurring.
4. If your roll of two dice resulted in a score of 3, 4, 5, 6 or 7,
please click now.
A. 3
B. 4
C. 5
D. 6
E. 7
5. If your roll of two dice resulted in a score of 7, 8, 9, 10 or 11,
please click now.
A. 7
B. 8
C. 9
D. 10
E. 11
(Yes, the 7’s get to answer both questions.)
Note: depending on polling system being used, you may be able
to gather the data directly. These questions work for multiple
choice type clickers.
6. If your roll of two dice resulted in a score of 2, 7 or 12, please
click now.
A. 2
B. 7
C. 12
(Yes, the 7’s get to answer again!)
8. Imagine there is only one atom.
• Two possible arrangements when the valve is opened.
• Probability is ½ that the atom will be found in the left bulb.
• Just as with the dice, each of the possible arrangements is called a
microscopic state, or a microstate.
Let’s relate the concept of microstates and
probability to entropy and chemical systems:
9. Now, add a second atom.
• There are now 4 possible arrangements or 4 microstates.
10. With three atoms there are 8 microstates.
What is the relationship between the number of microstates, the
number of positions and the number of atoms?
number of microstates = nx
where n = number of positions and x is the number of molecules
11. Consider the ways that 4 atoms can be arranged…
# of microstates = 24 = 16
All 4 atoms in one bulb
2 possible configurations, or microstates
12. 3 atoms in the left and 1 atom in the right
3 atoms in the right and 1 atom in the left
4 possible configurations, or microstates
4 possible configurations, or microstates
13. Two atoms in the right and two atoms in the left.
This distribution has the greatest number of microstates
and is the most probable distribution.
6 possible configurations, or microstates
14. On a macroscopic scale, it is much more probable that the atoms
will be evenly distributed between the two flasks because this is
the distribution with the most microstates.
15. Ludwig Boltzman related the number of microstates (W) to the
entropy (S) of the system:
S = k ln W
where k = Boltzman constant = 1.38 x 10-23 J/K
• A system with fewer microstates
has lower entropy.
• A system with more microstates
has higher entropy.
16. The 2nd Law of Thermodynamics can be restated as follows:
An isolated system tends toward an equilibrium macrostate
with maximum entropy, because then the number of
microstates is the largest and this state is statistically most
probable.
17. Consider two spins.
Assign a value of +½ and a value of –½.
How many microstates are possible?
How many macrostates are possible?
Which macrostate is the most probable?
22 = 4
+½ + +½ = 1
+½ + -½ = 0
-½ + -½ = -1
Probability
¼
¼
½
+½ + -½ = 0
It is more probable to have a pair of electrons with unpaired
spins than with paired spins.
18. lower entropy greater entropy
Positional probability: depends on the number of positions
in space (positional microstates) that yield a particular state.
lower positional probability higher positional probability
19. Which distribution of 6 particles into three interconnected boxes
has the highest entropy?
A.
B.
C.
D.
21. Select the correct statement:
A. The solid state has lower positional probability and
greater entropy than the gas state.
B. The solid state has higher positional probability and
greater entropy than the gas state.
C. The solid state has lower positional probability and
lower entropy than the gas state.
entropy solid < entropy liquid < entropy gas
22. Ludwig Boltzman related the number of microstates (W) to the
entropy (S) of the system:
S = k ln W
where k = Boltzman constant = 1.38 x 10-23 J/K
• A system with fewer microstates
has lower entropy.
• A system with more microstates
has higher entropy.
23. The use of entropy in predicting the
direction of spontaneous change in states
is in the
Second law of
thermodynamics:
For any spontaneous process, the entropy
of the universe, ΔSuniverse, increases.
