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# Entropy intuition

Introduces second law of thermodynamics. A discussion of entropy change in terms of heat and microstates . Created by Sal Khan.

## Want to join the conversation?

• So if I take the example of a TV screen with white noise has every pixel randomly black or white, with equal amounts of white and black pixels, the entropy would be at a maximum, even if the pixels randomly organize themselves at some point? What would low entropy look like in such a system?
• You're right - when half the pixels are black and half are white, this is the highest entropy. The reason for this is that, if you consider every different possible arrangement of pixels that would give 50% black and 50% white, there are more possibilities for this 50/50 split than for any other percentage split. This makes the 50/50 split the most probable, and thus it has the highest entropy.

You're right that some of these possibilities might look 'organized', for example a bunch of black pixels grouped together (though this arrangement is improbable). This would be one of many microstates (i.e. individual possible arrangements of pixels) that contributes to the maximum entropy macrostate (i.e. the big picture that there is a 50/50 split between black and white pixels). If you limited yourself to only having a bunch of black pixels grouped together, however, then the entropy would be lower, since the probability of this happening is lower once you introduce a restriction.

In the pixel system, low entropy would be if all of the pixels were black or all of the pixels were white.
• If you're cleaning the room, aren't you the engine, much the same way the AC compressor is?
• I think so too- and if you expend energy to put things in drawers and closets, aren't you decreasing entropy, or increasing order, by confining the things - ie- by limiting the places they can be in the room, the way intermolecular or ionic forces might order particles in a crystal?
• Is being in Ordered state the same thing as being in least state of energy? If so then isn't it the natural tendency for matter to be in the least state of energy? So is itnot possible for it to return to ordered state unlike .
• First, keep in mind that energy and entropy are TWO different things. Secondly, lay out all the variables in whatever problem you are dealing with - then if you calculate entropy of the universe, no matter what situation you are dealing with, you will always find the entropy of the UNIVERSE increasing. When talking about entropy, it is essential to be specific about your problem. Remember the example of hot outside and cold inside with an air conditioner that Sal talks about? If you miss out the heat that the air conditioner loses, you mess up.
• Is there a reason you use Q for heat? In my textbook, H is used for enthalpy..which ones the industry standard?
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• Q and H refer to subtly different things. Q represents the heatflow in and out of a system while H is the overall energy within a system. You'll therefore usually see chemists using H (and consequently ΔH) instead of Q because enthalpy allows them to disregard what's going on outside of the system, something Q would make them keep track of.

Side-note: Q is a inherently a path variable while H is a state variable. However, adding Δ to H makes it a path variable since it is now keeping track of changes in the system.
• This video and several others on thermodynamics discuss path variables and state variables. Are these terms applicable only to thermodynamics? Is there a mathematical definition? I took calculus and differential equations many years ago, but I don't remember these types of variables being covered. What branch of mathematics covers this? Are they discussed on any of Kahn Academy's math videos. Thanks!
• This appears in multivariable calculus. It isn't exclusive to thermodynamics, it also appears when you're defining potential, for example. A 2 variable (x and y) function will be path independent if (∂²f/∂x∂y) = (∂²f/∂y∂x), I don't remember the general definition for n variables :p, but I think it's something analogous (like ∂³f/∂x∂y∂z = ∂³f/∂x∂z∂y = ∂³f/∂y∂x∂z = ...). The idea is that a small change in f will be the same independent of the order in which you took the small steps in x,y,z,w,...
• If entropy depends on volume (more the space, more potential states the particles have) then why isn't it included in the equation for entropy?
• will the entropy of the universe continue to increase forever and continue to get more chaotic to infinitum?
(1 vote)
• That is a theory, that one day, nuclear forces will cease to stop entropic forces, and all matter in the universe will decay into a quantum soup of protons, nuetrons, and electron.
• Okay, so we're learning entropy in AP Bio and it is really confusing me. I would appreciate if someone could explain:

Aren't "ordered" and "disordered" subjective terms? How do we define something that is ordered as opposed to disordered? I can understand why going from water --> gas is an increase in disorder, but I've also heard that any phase change in general increases disorder, so that would imply that going from a gas to water would also increase disorder, even though...it wouldn't?

I've also heard that entropy and the Second Law of Thermodynamics do not apply to open systems (like humans and ecosystems)--is this true? If so, why? If not, why?

Thanks!
• Good question. I agree that "ordered" and "disordered" are subjective. "Structured" vs "unstructured" might be a little better. A solid has lots of bonds, so it has the lowest entropy (the most structure) of any phase. The molecules of a gas are the least interacting and most free to bounce around at random speeds and directions, so gas has the highest entropy (least structure). I'm not sure what the context was where you heard that "any phase change in general increases disorder". I would say gas to liquid and liquid to solid always lower the entropy of the material being cooled. Now, if the WHOLE SYSTEM is taken into account, then almost every process increases the entropy of the universe (Second Law). So when you put a cup of water in the freezer and it becomes ice, well the entropy of the water was reduced, but the refrigerator was running and removing the heat from the water and blowing that heat, plus some extra heat, into the kitchen, so the entropy of the air in the kitchen increased by MORE than the entropy of the water decreased. This is also basically the answer to your last question about organisms. They are an open system, like the refrigerator, so they can keep their entropy low but only by consuming low-entropy food and then emitting high-entropy waste into the environment. The entropy of the universe increases, but not the entropy of the organism. It's not that "the laws of thermodynamics don't apply to humans". They do. It's just that the Second Law only applies to closed systems, and humans are not closed systems.
(1 vote)
• i don't get why T1 is bigger than t2
• That was by definition, he defined 2 bodies touching. One hot (T1, magenta), one cold (T2, cyan). He defined all this at
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• I know the "clean room : dirty room room" example is not that good, but I was wondering about what Mr. Khan meant when he said Mircrostates. ()-ish. Everyone says that the universe progresses from order to disorder but does it ever return to its original order, or is it only when energy is applied? "Room goes from clean to dirty, but will eventually return to dirty" Because systems can ONLY maintain molecular organization if energy is added. "You use energy to clean room" - Thanks