# Entropy: Explaining the Paradox of Energy in School Thermodynamics

• Rockazella
In summary: FZ+ Entropy is simply a measure of spread of energy. Say, let a billiard ball bounce withing half of pool table (say, by having a stick dividing table on two and not letting ball into the other half), and then remove the stick and let the ball to take over entire pool - the ball will do that. We call this "entropy increase". Whenever you give to a physical system more states, it'll occupy them too along old states. Arithmetic of this is what we label as "law of increase of entropy" or "law of increase of disorder" or "heat goes from hot to cold", etc.

#### Rockazella

In school we just started a unit on thermodynamics. So far entropy was only briefly talked about. On first impression it seemed to me that the idea of entropy sort of goes against the definition of energy. Energy being the ability something has to do work, and entropy being energy that isn't available to do work. Doesn't really make sense to me..can anyone explain?

Also, if the entropy in a closed system is suppost to go up whenever an energy change takes place, wouldn't that go against energy can never be created or destroyed?

Mix hot water and cold water. The net result is warm water (same amount of energy). Entropy has gone up - you can't unmix into hot and cold in the closed system.

The fundamentals of thermodynamics is that when we do work, we exploit an energy gradient. (usually temperature) The nature of energy is to move towards a point where all the energy is in equilibrium, or equally distributed in all places - that is said to be at maximum entropy, or disorder. Heat engines use this as power. Consider a hydroelectric plant... it uses the imbalance in gravitational potential to generate power. All of our other engines work this way. Now, at a point of maximum equilibrium, no work can be done. The energy is present, but there are no longer any relative potentials. In order to restore imbalance, work must be done INTO the system ie. raise the water up. To do this, you would have to raise entropy somewhere else, and lose additional power from equilibrium. Hence the Second Law.

Originally posted by FZ+
The fundamentals of thermodynamics is that when we do work, we exploit an energy gradient. (usually temperature) The nature of energy is to move towards a point where all the energy is in equilibrium, or equally distributed in all places - that is said to be at maximum entropy, or disorder. Heat engines use this as power. Consider a hydroelectric plant... it uses the imbalance in gravitational potential to generate power. All of our other engines work this way. Now, at a point of maximum equilibrium, no work can be done. The energy is present, but there are no longer any relative potentials. In order to restore imbalance, work must be done INTO the system ie. raise the water up. To do this, you would have to raise entropy somewhere else, and lose additional power from equilibrium. Hence the Second Law.

Can someone give an intuitive reasoning for why the entropy of a black hole is equal to the (event horizon) surface area?

This is the 1974 Bekenstein result that kicked off all the current work in quantum gravity (hawking's BH temperature and radiation result followed close on Bekenstein.) It is a major landmark in contemp physics. There has to be some, at least
*some*, intuitive content.

Sometimes entropy is associated with the idea of information. Why is this?

Originally posted by Rockazella
In school we just started a unit on thermodynamics. So far entropy was only briefly talked about. On first impression it seemed to me that the idea of entropy sort of goes against the definition of energy. Energy being the ability something has to do work, and entropy being energy that isn't available to do work. Doesn't really make sense to me..can anyone explain?

Entropy is simply a measure of spread of energy. Say, let a billiard ball bounce withing half of pool table (say, by having a stick dividing table on two and not letting ball into the other half), and then remove the stick and let the ball to take over entire pool - the ball will do that. We call this "entropy increase".

Whenever you give to a physical system more states, it'll occupy them too along old states. Arithmetic of this is what we label as "law of increase of entropy" or "law of increase of disorder" or "heat goes from hot to cold", etc.

Energy is not lost, it is just spread over those states which become available. Just becase there is no difference between "new" and "old" states.

In order to restore imbalance, work must be done INTO the system ie. raise the water up. To do this, you would have to raise entropy somewhere else, and lose additional power from equilibrium. Hence the Second Law.

FZ,
Would you mind giving an example of that?

Originally posted by Rockazella
FZ,
Would you mind giving an example of that?

As an example, an accidentally dropped egg splatters in a cup. the reverse process, a splatered egg reforming into a whole egg and jumping up to an outstretched hand, will never happen on it...
if you puncture a helium-filled balloon in a clsed room, the helium gas spreads throughout the room--but the individual helium atoms will never clump up again into the shape of the balloon.

That part makes sence. What I don't get is in FZ's post he said work needed to be done into the system to restore imbalance or potential difference. Doing that work would raise entropy somewhere else. How does doing work in a system raise entropy in some part of it?

Originally posted by marcus
Can someone give an intuitive reasoning for why the entropy of a black hole is equal to the (event horizon) surface area?
...

Why should the entropy of a black hole be proportional to its surface area and not proportional, for instance, to its mass, or volume?

There is an idea here----the log of the number of microstates all of which appear the same on a macro level----or? what has happened to the idea of entropy? It must be evolving, getting broader or deeper, for it to be possible to identify it with the area of a black hole. this is one of the most influential results in contemporary physics, it has to mean something. you can't just keep on talking about popping a balloon full of helium and ignore this other aspect of entropy.

Anybody have a clue? Mentors?

let's get some of mc hawking's expertice on the subject:

Entropy, how can I explain it? I'll take it frame by frame it, to have you all jumping, shouting saying it. Let's just say that it's a measure of disorder, in a system that is closed, like with a border.
It's sorta, like a, well a measurement of randomness, proposed in 1850 by a German, but wait I digress. "What the **** is entropy?", I here the people still exclaiming, it seems I got to start the explaining.

You ever drop an egg and on the floor you see it break? You go and get a mop so you can clean up your mistake. But did you ever stop to ponder why we know it's true, if you drop a broken egg you will not get an egg that's new.

That's entropy or E-N-T-R-O to the P to the Y, the reason why the sun will one day all burn out and die. Order from disorder is a scientific rarity, allow me to explain it with a little bit more clarity. Did I say rarity? I meant impossibility, at least in a closed system there will always be more entropy. That's entropy and I hope that you're all down with it, if you are here's your membership.

Defining entropy as disorder's not complete, 'cause disorder as a definition doesn't cover heat. So my first definition I would now like to withdraw, and offer one that fits thermodynamics second law. First we need to understand that entropy is energy, energy that can't be used to state it more specifically. In a closed system entropy always goes up, that's the second law, now you know what's up.

You can't win, you can't break even, you can't leave the game, 'cause entropy will take it all 'though it seems a shame. The second law, as we now know, is quite clear to state, that entropy must increase and not dissipate.

Creationists always try to use the second law, to disprove evolution, but their theory has a flaw. The second law is quite precise about where it applies, only in a closed system must the entropy count rise.
The Earth's not a closed system' it's powered by the sun, so ------- That, in a nutshell, is what entropy's about, you're now down with a discount.

Entropy is spread of energy over all available states.

Give a system more states - energy will spread over them too (system does not know which states are "new" states and which ones are "old" states).

So, it is all just statistics (=arithmetic of combinations and permutations):

http://www.physics.ubc.ca/~birger/boltzmann/node3.html

Originally posted by Rockazella
That part makes sence. What I don't get is in FZ's post he said work needed to be done into the system to restore imbalance or potential difference. Doing that work would raise entropy somewhere else. How does doing work in a system raise entropy in some part of it?

The explanations you've gotten so far are pretty good. A simpler thing would be to say that energy goes from where there's more to where there's less. And, since everything (all matter) is made of energy, all things follow this behavior.

For example, you can't heat your cup of coffe buy setting it out in the snow. Now, you might reason, "the temp. of the snow is not absolute zero, so there is some heat in it, this could go into my coffe". Entropy is there to say, "but it won't". Same way, you can form a tall collum of water by puling a glass upside-down out of a full sink. Break the seal and release the forces that hold the water in place, and it will fall until it is a level surface again. Press the glass (right side up) down into the water, and you can make a dent. Remove the glass, and the water level of the entire sink will lower just to fill in that dent. If I may wax Biblical; "Every valley shall be exalted, and all the mountains and hills made low. The crooked shall be made strait, and the rough places plain."

So when you take water from a water fall to make ellectricity, you are trapping some energy on its way from "up high" to "down low". But you can't be perfect; you can't catch ALL of that energy. So, if you used the ellectricity you get from the dam to operate a water-pump to try to put all the water back, you'll find that even if you have the most efficient dam and pump possible, you don't quite have enough juice to do it. You'll need a little more from somewhere (maybe another waterfall).

Maybe you could use a bucket to put the rest back if it's a small enough amount. But only if you eat a good meal first, taking energy from the ecosystem and burning it as fuel for your muscles. Either way, energy is lost out into the cosmos. So, everything you do serves at least two purposes; 1)the task you intended to accomplish, and 2)heating outer space!

Originally posted by Rockazella
That part makes sence. What I don't get is in FZ's post he said work needed to be done into the system to restore imbalance or potential difference. Doing that work would raise entropy somewhere else. How does doing work in a system raise entropy in some part of it?

Imagine you have a box with two compartments. The compartments are able to transfer heat, but at a slow rate. The box is also insulated from the outside world.

If you put 'hot stuff' in one side and 'cold stuff' in the other side, eventually they will settle into an equal temperature 'warm stuff' on both sides. The entropy of the system has increased.

If you then hook up a temperature seperating machine (like an AC/heat pump combo) you could separate the hot and the cold into sides again. The only problem is that doing so would generate entropy in the environment (because the machine needs power to run).

hopefully that makes some sense...

Universal Entropy

Hello students (Newton1, FZ+, jb, enigma) and 38 year old Lurch.

Entropy, as a chemist sees it, does pertain to irreversibility of many processes that can be quantified as T[del]S.

On the other hand, to some physicists, entropy is a measure of disorder in a system. When the obvious chaos in natural systems is considered without any balancing of the well-ordering aspect of that natural system, it is conceivable that universal entropy could be called ever-increasing. The epitome of chaos is the permanent and continuously forever-increasing light rays in the universe. The epitome of well-ordering is the natural event of the conversion of light energy into indestructible matter and antimatter. That includes "dark matter" that continues being alive with ever-cycling quantum orbitals.

There is no argument here that universal entropy is not ever-increasing but that, without an accounting for well-ordering, quantification of universal entropy is not possible.
Thanks for your audience. Cheers, Jim

Increase of disorder is just s statistical (=arithmetical) law. You can't reverse it.

Nor does arithmetic (statistics, or entropy) shows or indicates mystical "direction of time". (Indeed, reverse time, and system will still occupy all available states.)

## 1. What is entropy?

Entropy is a measure of the disorder or randomness of a system. In thermodynamics, it is often described as a measure of the unavailable energy in a closed system.

## 2. How does entropy relate to energy?

Entropy and energy are closely related in thermodynamics. Entropy is often referred to as the "paradox of energy" because as energy is transferred or transformed, the overall entropy of a system tends to increase.

## 3. What is the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system always increases over time. This means that energy tends to disperse and that processes move towards a state of greater disorder.

## 4. Can entropy be reversed?

In a closed system, entropy can never decrease over time, but it can be reversed in an open system. For example, plants are able to decrease entropy by taking in energy from the sun and using it to create order in the form of glucose molecules.

## 5. Why is entropy important in science?

Entropy is a fundamental concept in thermodynamics and plays a crucial role in many scientific fields, including chemistry, biology, and physics. It helps us understand the direction of energy flow and the changes that occur in systems over time.