First of all, an answer: the Boltzmann constant.
Entropy is also not understood by many high school teachers, although it is of fundamental importance for the understanding of natural processes.It should therefore find its way into the minimal scientific knowledge of the grammar school. Teachers should not (only) hide behind formulas, but explain entropy by simple and to see-through examples.
In school physics lessons, conservation variables are taught, e.g. energy, impulse, mass and charge.Entropy is the first time you have come across a directional size in the classroom. It is therefore necessary to clarify this concept and to distinguish it sharply against the familiar conservation variables, in particular energy. If you don’t value the mathematical basics, you don’t read the italic print
Here we see two stones.
The left stone was heated to 100 degrees Celsius in the oven, the other one has room temperature (well, with me it’s a bit warmer), so it’s relatively cold. Both stones are right next to each other, so they touch each other. If you go out of the room for a long time to write an answer to Quora, for example, and then come back, you find that the eone stone cooled down, the other one warms up. In theory, both stones have the same temperature; purely mathematically, they would have to be 60 degrees warm.But now they don’t come with the objection that both stones cool down over time and then are no longer 60 degrees warm – we shouldn’t carenow.
This is the basic principle: before there was an order = low entropy,one stone was hot, the other cold, a rather unlikely state when they were lying next to each other they exchanged.After the heat equalization there is a state of low order = high entropy, it is much more likelythat two adjacent stones have the same temperature than that they have different temperatures.
For every person, hot/cold sensations are practical experiences.You have learned what temperature is and that you measure it with a thermometer.
With the term heat, it is already a little more difficult term.But most of us go with the terms calories or joules as a matter of course.These are the units of measurement of heat or rather the “heat quantity” .
Stored energy we converted in the body.The general rule is this: the energy E of a system changes when mechanical energy (“work”) is added to or dissipated by mechanical energy (“work”) sW and/or heat .Q: E = “W ” + “Q” (i.e. formula stuff).This equation, which is nothing more than a generalized energy set, is often called the “first main proposition of thermal theory”. Heat is an expression ofenergy.
(Well, the physicists… when i am given energy in the summer I sweat )
Let’s take a look at a container with ideal gas: it consists of atoms that move “like wild” through the room.
They spread in all directions at different speeds. At the limits of the container of the gas, the atoms are reflected, changing their velocities and colliding with other atoms. Even if the speeds of the individual atoms change constantly, the impression of an “disordered” movement remains. They’re still simmering like wild!
If you add additional energy, heat, to this gas, the speeds increase. The disorder remains or becomes even greater in this disordered system.
If you channel the gas and drive it, the atoms of the gas all fly at the same speed as soldiers, then you have an orderedsystem.
This also applies in mechanics, in orderly movements. When a stone falls, all its atoms fall at the same speed and in the same direction.
The associated energy, kinetic energy or kinetic energy of the stone is calculated from its total mass M and its velocity v to: E stone = 1/2 M v2. But STOP: also to the disordered movement in a gas one can assign a total energy, namely the sum of the energies of the individual gas atoms EGas = 1/2 m vi2), where m is the mass and vi the velocities of the N individual atoms.
The velocities vi differ from each other in direction and size.
If all molecules were moving in the same direction and at the same speed, vi = v would be and the formula for the stone would be m = N m. And now comes the consequence:
To define an ordered motion, one only needs the knowledge of a velocity, while the state of the gas at a certain time is only fully determined when all N velocities are known.The energy that belongs to the disorderly movement of atoms in a gas tank is also called the internal energy, which could also be called thermal energy. We now summarize the result in the memorization of heat is energy in disordered motion.
What is common to the examples of falling stone and heated gas is that it is the same form of energy, namely kinetic energy.The difference between the two phenomena is the degree of order for which we need to introduce a new measure. This will be entropy.
Let us ask ourselves, what is order?and look at your desk. Ordinary or not? You can say yes or no, but to measure it, you need an verifiable system.
The most neat possible state of your desk is when everything is in place, provided for this purpose, and refer to this as TOP (or otherwise with the letter ” the number of possibilities to arrange the objects.For the most practical arrangement for you, therefore, the following applies to the
Now someone is changing the order without paying attention to your system.
It may adjust the mouse of the computer. Since he has many ( N-1 ) objects in front of him, he can place the mouse in front of, between or behind objects.Thus, it has a total number ( N) of possibilities, (N) Only one of them is the one you want.
Now the next one comes and grabs something, this person, (N-1) has other options where he has to access.Accordingly: if two persons each reset an object to any position, the first (N-2) sees objects in front of him and thus (N-1) has possibilities to place the mouse.The second reader then has the situation as above, i.e. other(N) possibilities, (i.e.total: N-1.
And if then their little son is still playing around, then everything can be in any possible order (wherethe the number of these sequences is:)
Then it can look like this:
The number of items is very fast, very large: for only 10 items you have 3.6 by 10×6 possibilities.
For a very general system, we formulate the phrase:
The degree of disorder of a system is characterized by the number of possible states that the system can occupy.
鈥?= 1 means maximum order.
The most likely condition is the one with the greatest possible entropy S, i.e. the greatest possible disorder.
In this example, we learn important characteristics of disorder:
- If you leave the arrangement on the desk without a system to everyone, the disorder will increase over time, never decrease.
- There is a maximum value of disorder, that of if everything is possibly obscured.
Even if other users of the library change the order of the books, the degree of disorder remains, because no book knows where it stands.
And now maths is coming again….’tschuldigung!
Not only the number of possibilities indicates a measure of the disorder, but also every monotonously growing function f.For this, S called S = kB ln (A) is used and this is not without reason.The logarithm function has the important property that the logarithm of a product is equal to the sum of the logarithms, ln(a b) = lna + lnb. For two systems that have nothing to do with each other, the number of possibilities is equal to the product of the individual possibilities.
(Systems 1 and 2 S = S1 + S2) . The multiplicative constant kBin of the definition of entropy is arbitrary in a certain sense. With the Boltzmann constant, many formulas become simpler and these are applied in the statistical physics of heat.
For practical implementation, this would still be the desk of your wife/husband. If your son “strikes” again!This is because two desks that are not in contact multiply the number of possibilities.The following statement, also called “second main principle of thermal theory”, contains the most important characteristic of entropy: in a closed system, entropy never decreases. (“By itself, disorder never decreases, I have to intervene”).
S > 0. From the context of entropy and disorder, this statement is plausible But plausibility is not yet proof.However, the dS>0 property can be derived under certain conditions from the context of disorder and entropy.
Since entropy in a closed system always develops in one direction, we want to call entropy a directional size, to the difference from the energy, which is a conservation sizefor the same system.
The entropy of a system depends on its properties, e.g. its
- Energy e
- its volume V,
- its particle number N and, of course, from its
- material composition
and changes with these parameters.
That is why we write S(E,V,N,..) .
You can now track how the entropy of a system changes when you change the individual parameters. The most important case is the following:
If you change the energy E in a system by a .E and keep all other parameters constant, the entropy changes by 鈥 = E / T, where In T is the absolute temperature.This formula is also often written with “Q” instead of “E”, where “Q” is the heat inwhichory or dissipated. However, this is irrelevant.
When my wife and I go for a walk in winter, she sometimes asks: Do you eat?Why should I? Or did she just mean, did you dress thick enough?It’s really coldtoday!. It certainly seems familiar to you!
Yes, we freeze because it is cold around us.Now a physical socrates could follow up: “Sure, it’s cold, but whatdoes the cold of the air have to do with our freezing?” He would be told that you would freeze because some of the body heat would be emittd to the air.
But why, he would ask further, does the body heat flow away from the person?
We have the answer –entropy – ready, but we still have to work it out.And so we are at the beginning of the answer with the stones.
Nun, however, somewhat more general: two systems, which we distinguish by indices 1 and 2, are brought into heat contact.The overall system from the two systems remains closed to the outside world. Before contact, the subsystems have the energies E1 and E2 and entropies S1 and S2, wherethen for the whole system applies E = E1 + E2, S = S1 + S2. A heat quantity of Q flows spontaneously from system 1 to 2 via the heat contact, i.e. without our intervention.
Due to the maintenance of energy, the total energy does not change, so that the energy E’ applies after the heat contact E’ = (E1 – Q) + (E2 + Q) = E
The energy ‘Q’ which has flowed from System 1 has flowed into System 2, so that the new total energy E’ is no different from E.However, the entropy S’, which results from the overflow of the heat , differs from the initial entropy S, because S’ = S1 + (—Q)/T1 + S2 + Q /T2 = S + Q (1/T2 – 1/T1). Now the basic message of entropy comes into play, namely that in a closed system entropy always increases. Therefore, the difference S’-S must be positive. However, if the positive energy of Q flows spontaneously from system 1 to system 2, this can only happen if (1/T2-1/T1) is 0, i.e. T1 . T2, i.e. if it flows from the system with a higher temperature to the one with lower.
And the note: In a closed system, heat spontaneously flows only from the hotter to the colder body.
This knowledge corresponds to our experience.In winter, heat flows from our body into the colder environment. That’s why we’re freezing. So that this doesn’t happen so quickly, the woman asks: Have you dressed warm enough?
Now we have noticed that the heat always flows only in one direction: from hot to cold.This is the goal of everything, always to produce the state of maximum entropy. The heat flow will not end until the temperatures of the two bodies are equal, thus balanced.
Heat is energy in disorder.In a colder system, the molecules move on average more slowly than in a hotter one. And at absolute zero, nothing moves at all.
With the realization of the importance of entropy, fear and terror spread in literature: Einstein also insinuated that the universe is a closed system, so entropy is constantly increasing. At some point, the universe would have to reach a state in which a complete temperature balance between all bodies has occurred.There is no KALT and no WARM… everything is the same. All stars are extinguished
Today, physics doubts you about everything, including heat death.
In any case, we know that the sun will be shining for several billion years, thus maintaining all processes on Earth. However, in a very distant future, the universe could actually suffer a heat death. But beware: there are also doubts that the universe is actually a closed physical system.
Oh what else….I don’t see the forest for the trees mehr…..an all the math cracks… please correct.