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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?

• A small question, I think I get how an increase in volume increases entropy, but now I understand a little more this concept... can somebody explain to me how come an increase in temperature increases this combination of states? •   When the temperature of a gas is increased, the molecules have higher kinetic energies. When the molecules move around faster they can configure themselves in more ways than they could have if they had less kinetic energy. More specifically, molecules in an ideal gas follow Maxwell-Boltzmann statistics which imply that the molecules' velocity distribution broadens as the temperature of the system is increased.
• Can you do a lecture series on Shannon's information theory? • 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 it would be nice to add that the bouncing ball also loses energy by friction with air. I mean, I know for some people is obvious, but just in case somebody doesn't know.

-J. Garcia • 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?
(1 vote) • 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!   