शनिवार, 29 मई 2021

what is entropy ?


why energy flows in certain directions and in certain ways  ?

a lot of  the concepts described by thermodynamics seem like common sense but there 

 we won't get into the math but we should be able to describe these laws conceptually the first law described in the most basic way highlights conservation of energy .

 

it is not created or destroyed it only changes forms from potential energy to kinetic energy to heat energy etc.

 while we have found this to be untrue on the quantum level for chemists it does just fine however there seems to be a preferred direction in which energy flows from one form to another.

 in order to understand why we look at the second law the second law introduces a new easily describe entropy as disorder and the second law states that the sum of the entropy of a system and its surroundings must always increase in ,other words the entropy .

 

within a system there is also a tendency to go towards higher entropy the classic analogy is that your bedroom will over time become messy but it won't suddenly become neat.

 another way to look at this is to say that entropy is a measure of how dispersed the energy of the system is amongst the ways that system .

 an ionic solid compared to the same substance as a liquid clearly the solid state is more ordered and the liquid state is more disordered or higher in entropy to describe the solid state using computer.

 

the liquid state you would need to simply describe the volume of liquid and the shape of the vessel because the motion and configuration of the molecules are random that's far less information that needs encoding which is a way of rationalizing why increasing the entropy of a system is thermodynamic ally .

 

entropy influence heat will flow from a hot coffee cup into the table or your hand because the heat energy will be more disordered if more dispersed this is why heat spontaneously flows from hot to cold and not the other way around

entropy the third law states that are perfectly crystalline solid at Absolute Zero has an entropy of zero as this is the most ordered state the substance can be in entropy is measured in joules per Kelvin note .

that entropy is not a measure of energy itself but of how energy is distributed within a system it is enthrall the thermodynamic quantity we learned about before that is more accurately describing the energy of a system as we will see enthrall and entropy intricately relate to tell us something about the Gibbs free energy of a system .

 

whether a process will be spontaneous or not meaning if it will simply happen on its own change in Gibbs free energy is given by this equation which includes change in enthalpy change in entropy and  temperature if Delta G is negative the process is spontaneous if positive it is non spontaneous .

 

favorable and delta s is positive which means an increase in entropy which is also favorable a negative minus a positive will always be negative or spontaneous.

 

two is favorable we have to do some math if Delta H is positive or endothermic that energetic unavailability could be outweighed by the other term if the process is en tropically favorable and  since T is here this factor will increase with a larger T so  tropically favorable processes are more likely to be spontaneous at higher temperatures conversely.

 if it is energetically favorable but en tropically unfavorable the entropy unavailability will be minimized at lower temperatures this is a very important equation to understand because it describes all of the spontaneous processes in the universe.

 

there are those who incorrectly use entropy and the second law of thermodynamics to imply that order can't happen spontaneously .

they are miscible with polar water molecules but soap molecules have polar heads and long non polar tails which allows them to spontaneously form structures called micelles .

these are spheres where the soap molecules orient themselves with the polar heads facing out in order to maximize ion dipole.

 interactions with water molecules that bring the system to a lower energy and the non polar tails will all face in trapping the dirt by making a network  interactions the dirt trapped in the my cells washes away because the micelle as a whole is water-soluble .

due to the polar heads facing out that's how soap works and that's also how highly ordered structures can form spontaneously if by enthalpically favorable or energy storing processes in this way systems can defy entropy on the small scale.

 

the second law does hold true in that the entropy of the universe is always increasing let's check comprehension

…………………………………………..

 entropy is often described as a  measurement of disorder that's a convenient image but it's unfortunately misleading for example which is more disordered a cup of crushed ice or a glass of room-temperature.

 

another way of thinking about it through probability this may be trickier to understand but take the time to internalize it and you'll have a much better understanding of entropy consider two small solids which are comprised of six atomic bonds each in this model .

 

it is  turns out that there are numerous ways that the energy can be distributed like

 two solids and still have the same total energy in each each of these options is called a micro state for 6 quanta of energy in solid a and 2 in solid B there are 9702 micro states of course .


there are other ways our eight quanta of energy can be arranged for example all of the energy could be in solid a and none in B or half in a and half in B if we assume that each micro state is equally likely we can see that some of the energy configurations have a higher probability of occurring than others that's due to their greater number of micro states.


 entropy is a direct measure of each energy configurations probability what we see is that the energy configuration in which the energy is most spread out between the solids has the highest entropy .


so in a general sense entropy can be thought of as a measurement of this energy spread low entropy means the energy is concentrated.

 

high entropy means it's spread out to see why entropy is useful for explaining spontaneous processes like hot objects cooling down we need to look at a dynamic system where the energy moves in reality .

energy doesn't stay put it continuously moves between neighboring bonds as the energy moves the energy configuration can change because of the distribution of micro states.


 there's a 21% chance that the system will later be in the configuration in which the energy is maximally spread out there's a 13% chance that it will return to its starting point and an 8% chance.

 that a will actually gain energy again we see that because there are more ways to have dispersed energy and high entropy than concentrated energy .

the energy tends to spread out that's why if you put a hot object next to a cold one the cold one

 will warm up and the hot one will cool down but even in that example…

 there is an 8% chance that the hot object would get hotter why doesn't this ever happen in real life it's all about the size of

 

the system our hypothetical solids only had six bonds each let's scale the solids up to 6,000 bonds and 8,000 units of energy and again start the system with three-quarters of the energy .

 

there's no mysterious force nudging the system towards higher entropy it's just that higher entropy is always statistically more likely that's why entropy has been called times arrow if energy has the opportunity to spread out.

 

 


रविवार, 2 मई 2021

quantum field theory'Higgs Boson'

 

"Quantum field theory " it also called classical quantum field theory"



 describing how the electromagnetic field at large distances acts on a hypothetical particle or a field…

 

If "p" is some small positive constant then "p", like all other integer or real numbers, must have a natural unit of measure, such as the pico-meter or quanta…

 

It follows that for any 2D sphere in 3D with two degrees of radius “R” and the center at coordinates a[i, j] R  = 0 and b[i, j] R  = 1 …

 we have the following alternative model that proposes the origin of the Higgs Boson (the particle responsible for the production of Z bosons) as the result of perturbation of the symmetry which consists of a single charged particle, i.e. one with charge i…

 This model is called the “weak model” because it generates a number of particles leptons and muons

 that do not obey the second law of thermodynamics, and so cause fluctuations in the macroscopic world…

 

 The existence of the Higgs Boson at its charge “I” is the crucial ingredient for our full understanding of the electro-weak theory, so it is that this particle is actually the one discovered…

 

With the development of electro-weak theory there is evidence that the energy scale of these fluctuations is on the order of  10 GeV, which at the energy of the synchrotron beam in the Large Hadron Collider(LHC) has lead to some doubt that the only thing generating the fluctuations is ELECTRO-WEAK MAGNETISM.

 

There is  fluctuations come from a cosmological solution of a hierarchy of super symmetric particles. However, the existence of that theory is not yet proven, and a number of other candidates have been proposed.

 

The above model defines the electron field, which can be described with the following equation…

 

The “PLANCK ENERGY” is around So, for "p" = 1/2.000 = 0.02 (the value of "p" that would correspond to such a configuration of matter), the energy per unit charge …

 

So, the energy of a proton of charge” I” at rest  is an approximation that is rarely used, because the proton’s electric charge varies from charge “I” to  high-energy proton charge.

 

Most of the time when physicists use the expression above, they find mean energy of an electron-positron pair.

 

 The pair state is sometimes also called a pion, which is similar to the lepton. Here, we introduce the particle called a positron, which is identical in mass and charge to an electron, but is heavier by about 1000 times.

 

The usual expression of an electron-positron pair (i.e. in which we treat electrons as mass less particles) is Here,” ζ” is the electron wave function, which can be written as either

 

Or Then... it follows that for the proton- collision to create a Higgs particle, there must be an energy imbalance…

 that is where the correction “δ” has to be made to account for the proton’s charge and the fact that it is mass less. The number “ ϕ” must be higher than 1/2 because the particle is bound by the electro-weak symmetry, and can not move freely.

 

The electro-weak theory of strong force (which makes up the other part of the gauge symmetry) is, similarly, fundamentally different from electro-weak theory, but can be described with the same unitary formalism. Here, the constants "E", "E", "E", "e", "e", "e", "e", "e" are used, and they correspond to

 

the “PAULI INTRECTION” (particles have an intrinsic momentum p p p p p p p p p p ),

 

the W or weak interaction (particles have an intrinsic momentum w w w w w w w w w w w ),

 

the  muon decay (particles have an intrinsic momentum μ μ μ μ μ μ μ μ μ μ μ μ μ μ μ μ μ ),

 

the bottom or neutrino interaction (particles have an intrinsic momentum n n n n n n n n n n n n n n n n n ), and

 

the photon interaction (particles have an intrinsic momentum p p p p p p p p p p p p p ).

 

 

How Supernova work ?

                          " Supernova a giant of universe "

 Somewhere in the universe a giant star is detonating creating a huge cosmic explosion called a  supernova, which are a big giant dramatic end to a star's life out with a bang called supernova …

 

we think it has to be at least eight times more massive than our Sun it's so easy to think of our Sun as this incredibly gigantic thing but our Sun is absolutely tiny compared to some of the giant stars in the sky …

we can see some of these giant stars with the naked eye and the tenth brightest in the night sky is a red super giant around fifteen times the mass of the Sun  is so big that if you're at a place in our own solar system it would stretch to the orbit of Jupiter ...


this is one of the biggest beasts in the galaxy on the verge of death Betelgeuse is less than 10 million years old but this huge stars days are numbered it's ready to blow and when it happen we can see the region behind sky brighten for 14 days, until it's nearly as bright as a full moon it is going to be one of the most spectacular shows in history …

  it could happen at any moment I mean this is the thing I often stand outside in my yard  look up at Orion and I see Betelgeuse…


 I'd like explode so what will make beetle juice goes supernova to understand a giant stars death we need to understand its life from the origin until the day it dies a star's life was a constant battle gravity is pulling in and energy pushing out the interior of a star is fusing countless atomic nuclei together atoms are ramming into each other getting very close if they get close enough…


 they'll actually stick and form a Giant bigger and every atom star fuses seventh and a half billion tons of hydrogen that amount of energy is roughly equivalent to about 100 billion atomic bombs per second that's a big-ass explosion this explosive energy threatens to blow the star apart but the stars own massive gravity keeps the lid on everything in the universe is a fight between the inward force of gravity and the outward force of pressure or energy…


 every single star in the sky even our own Sun is an incredibly dynamic battle ground in many ways stars are an explosion ,that are actually too big to explode gravity holds it together …


this battle between these two opposing forces determines the life and death of the star and this is where size matters the more massive the star the more gravity pushes inward and the harder the star has to push outwards to keep itself alive…


 very massive stars are like stars on steroids they have a lot of fuel to burn they're so powerful that they use up their fuel at a rapid rate massive stars like Betelgeuse are giant factories fusing lighter elements into heavier ones but the hard work doesn't start until their final years for around 90% of their life…


 they fuse hydrogen into helium but eventually the hydrogen starts running out in the core of a super giant star there's a sequence of fusion that goes from lighter elements to heavier elements and it gets faster and faster every step of the way the countdown to death…


 begins the inward push from gravity takes over raising the temperature in the core helium starts fusing into carbon there's enough helium to last about a million years but things start speeding up carbon gets fused into neon and that takes about a thousand years neon fusing into silicon, that takes about one year once it starts fusing silicon and iron that takes one day it gets more and more frantic …



  like a cooking contest show where as the clock is running down they're trying to do more and more things and they get more and more frantic until time's up the star is now in its death throes once iron production has started the clock is ticking towards the cataclysmic end of this star a giant ball of incredibly dense iron forms in the middle of the dying stars …


core of iron sphere is several thousand miles across and unbelievably hot it gets so  there the temperature almost becomes meaningless...


  we're talking about a billion degrees in the center of one of these stars this extreme heat is caused by fusion reactions more and more reactions create heavier and heavier elements and with each step less and less energy is produced until iron is created when it fuse iron nuclei together that takes energy …


it doesn't generate energy so once the core starts to fuse iron its basically stealing its own energy the growing iron core sucks more and more energy from the star gravity continues pulling in overwhelming …


the outward pressure from inside the star everything gets crushed to unimaginable degrees all of a sudden there's no nuclear reaction to support the star against the crush of gravity with nothing left holding it up the star is doomed gravity wins the edges of the iron core collapse trillions of tons of dense …


iron fall behind at a quarter of the speed of light the star has now less than one second left to live things start to fall apart really quickly the core collapse is so fast that the outer layers of the star don't even have time to react …


they're just hanging there it's kind of like wily coyote when a cliff collapses underneath them and he doesn't even fall until he notices the rest of the star collapses a trillion tons of gas curdled inwards …


following the iron think about the entire mass of a star that has been held up by nuclear reactions inside all of a sudden those nuclear reactions go away in a split second everything rushes into the middle and that sets off the most dramatic explosion in the universe…


 the spectacular deathblow can outshine all of the stars in the galaxy but there's a problem we still don't fully understand how a collapsing ball of iron and tons of falling gas create a giant fireball how this collapsing core triggers a massive explosion is one of the biggest mysteries in astrophysics.