ideal gas

Is information something real?

Normally one speaks of living things as beings that consume energy to survive and proliferate. This is of course not correct; energy is conserved, and cannot be consumed. Living beings intercept entropy flows; they use low-entropy sources of energy and emit high entropy forms of the same energy (body heat).

Can we burn information as fuel? Consider a really frugal digital memory tape, with one atom used to store each bit:

The position of a single ideal gas atom denotes a bit. If it is in the top half of a partitioned box, the bit is one, otherwise it is zero. The side walls of the box are pistons, which can be used to set, reset, or extract energy from the stored bits. The numbers above the boxes are not a part of the tape, they just denote what bit is stored in a given position.

The tape is a series of boxes, with each box containing one ideal gas atom. The box is split into two equal pieces by a removable central partition. If the atom is in the top half of the box, the tape reads one; if it is in the bottom half the tape reads zero. The side walls are frictionless pistons that may be used to push the atom around. If we know the atom position in the n-th box, we can move the other side wall in, remove the partition, and gradually retract the piston to its original position destroying our information about where the atom is, but extracting useful work.

Extracting energy from a known bit is a three-step process: compress the empty half of the box, remove the partition, and retract the piston and extract PdV work out of the ideal gas atom. (One may then restore the partition to return to an equivalent, but more ignorant, state.) In the process, one loses one bit of information (which side of the the partition is occupied).

A memory tape can therefore be used to power an engine. If the engine knows or can guess the sequence written on the tape, it can extract useful work in exchange for losing that information.

Reference:  Statistical Mechanics,  J. Sethna

can we all stop pretending that Majima hasn’t beat women and kidnapped A CHILD among other violent behaviour towards others in his lifetime pls  😇 😇 😇 😇 😇

Today I realized that the method I used for studying all my life was completely wrong and because of this, I failed Aerodynamics and Compressible flow. What I did was review the concepts in the lecture notes, and then after knowing I had a grasp of them, redo the problems in my lecture notes, text book examples, and HW problems. It sounded like a decent plan, right?

Except one thing: engineering and upper-level math exams rely on students solving problems they likely never seen before. They rely on testing the “on-the-fly” problem solving skills of students. That’s why professors make tests completely different from HW and lectures.

What I was doing was reviewing what I already knew. In other words, I wasn’t actually learning anything new or teaching myself how to tackle new problems: all I was doing was pointlessly redoing all the problems.

All that did was give me a false sense of confidence without actually learning anything new. In other words, this method only made me overconfident.

A different method would be something like this (under read more)

Keep reading

Crash Course aka. our saviours. 
(other crash course masterposts coming soon!)

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Biology 

Chemistry

Anatomy & Physiology

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Chapter 1.8 - Ideal Gas Law pt.1: the analogy  // Science Scribbles A-Level / IB HL Chemistry collection

(Click here for Ideal gas law part 2)

Hey again! I’m sitting in the children section of the library, so I decided that kids running around in a room would be a good way to visualize the ideal gas equation. Hope this helped you :D Stay tuned for part two, where I explain how to solve problems concerning the ideal gas law.

Remember the main difference between real gases and an ideal gas is that there are no intermolecular forces in an ideal gas - meaning there is no liquid phase when you cool it down. A real gas is similar to an ideal gas under high temperature and low pressure. :D

P.S. Lately I’ve started receiving a lot of requests, but unfortunately I do not have time to draw them all at once - so I’m only going to draw the ones that are most requested, I’m really sorry!

e)(o texts 08 - baeksoo
  • Baekhyun: My relationship with Chanyeol is sort of like an ideal gas,, high temperature and low pressure
  • Kyungsoo: Oh. So you found an educated way to say that you two in just for a good fuck?
  • Baekhyun: ( ͡° ͜ʖ ͡°)
“Every model is wrong, but some are useful”

The title of this post comes from the statistician George Box, and discusses how the mathematical models we use to analyse and predict the world cannot, by their nature as an understandable simplification, provide an exact model of the world. That is to say, they are “wrong”. However, the errors can be small enough that we can use the models to make predictions that hold up in real life, such as how much weight a bridge can carry. That’s where the “useful” part comes in. A good example of this is the ideal gas law. No actual gas follows this law, but under certain conditions, their behaviour is close enough that it doesn’t matter.


An important thing to understand is you can have multiple models to describe the same thing. There are a vast array of different climate models, for instance, and while they broadly agree with each other there are important differences in the details. Some of these are due to limitations on computing power and time available, some are focused on certain aspects such as aerosol production, and some are simply using a new method of modelling the world. When we are dealing with subjects as complex as human sexuality or the climate, we need to simplify them somewhat to allow us to grasp, if not the whole concept, as much of it as we can. All of these models will lose some important details, hence why they are all wrong, but some retain enough of the information that we can use them to understand the world.


Quite a few other statisticians have issues with this aphorism, but that’s not what I want to talk about here. I want to talk about gender and sexuality, and how we think about them. A common comment, when we look back at history and retroactively apply certain traits and sexualities to them, is that they wouldn’t have chosen those terms because their internal models are entirely different. Parts of Greece and Rome, for instance, are said to have defined the roles in male-male sexual encounters in terms of who is being penetrated and who is doing the penetration. Nowadays we would define both partners as homosexual, but they used a different model to understand their interactions than we do now. Different people at different times, different places and in different circumstances will use different models Someone using a different model of sexuality and gender to you is not inherently bad, or a judgement on you. I say not inherently because there are absolutely models that fail that include various points. I’m going to use asexuality here as an example because that’s my own experiences, but I think the general points could be modified slightly and applied to most sexualities.

Incomplete models, that is, ones that cannot handle the idea of someone not being attracted to anyone, fall into two catagories. The first is the “innocently” incomplete model; it is not that the person disbelieves in asexuality, but rather the idea that there is a gap in their empirical model of reality just hasn’t occurred to them. Contrast this to what we might call the “active” incompleteness model, where the model actively denies the existence of asexuality. I’ve encountered both of these kinds of incomplete model, as I suspect a lot of people have, and while the models are superficially similar how they react to the addition of an asexual person, or at least a person who claims they are asexual like myself. I put the “claims to be” part in there not as a way of throwing suspicion onto myself, but rather to acknowledge that people will claim I am lying or mistaken, that it is not possible to not be attracted to someone (you can insert “attracted to your own gender”, “attracted to more than one gender” or any other phrase you like there). Both models are wrong in the same way but the second model has a built in mechanism to avoid expanding the model to take into account an aspect of reality it had been lacking.

The other thing about models is that, once you get beyond a certain point, adding more detail doesn’t help unless you are using a model for a particular purpose that takes that detail into account. The various terms and models of sexuality that we classify as being on the asexual and/or aromantic spectrums are important if you are in a situation that requires the distinction to be made. Usually this means you are, or are interacting with, someone under that umbrella or wish to compare the model to your own experiences to see if you might be under that umbrella yourself. For most people most of the time, adding this detail just adds more mental computing power, and it is enough to acknowledge that, yes, you might need to increase the resolution on your model when dealing with that particular area, just like a meteorologist looking at one particular region will increase that resolution, but for now your model is wrong, but useful in that it acknowledges the existence of the asexual spectrum.

A really good example of this is the romantic/sexual attraction divide. This is a really important distinction in the ace community, between romantic asexuals and aromantic asexuals, and it is also useful for people outside of it (for example, there are bisexuals who are only romantically attracted to one gender), but is useless if your romantic and your sexual attractions line up. It can even muddy the waters by introducing an alleyway that might not lead you to a helpful option. That being said, the mere fact that such a model is not useful to everyone does not make it useless, merely that we need to shift our discussions about such models from “this is how the world works” to “here are mental tools to help understand the world and your place in it, and here are some possible limitations to them”.

I think gender is even more complicated to model than sexuality just because frankly I think the boundaries we have set on our concept of gender are incredibly fuzzy. The less well defined something is, the more difficult it is to model accurately, and we are really bad at defining gender. I think the three main models are as follows: biological gender, which states that someone’s gender is predetermined by their biology, usually chromosomes or genitals, social gender, in which gender is defined by the range of social expectations allowed with in it, and individual gender, in which gender is a property of each individual, that must be defined by each individual and social gender dynamics grow out of these definitions and their statistical distribution. Notably I have listed this in increasing order of immediate complexity. Biological gender claims to be less an explanatory model and more an empirical observation; these are the two types of people. I’m not fond of it for a couple of reasons. Firstly it doesn’t actually position the information in a new or useful way; it is merely a description of biological factors, and the distribution curves for what it tries to predict are large enough and include enough other factors that breaking it down this way doesn’t add anything. Secondly, it fails to account for intersex and non-binary people. The two ways it handles these are either to ignore them as edge cases, which works up until you need to include them as part of the model, or to outright deny their existence, which again, reduces the model’s effectiveness at describing reality. To make matters worse for this mode, it isn’t actually a particularly useful model day to day; when choosing what pronouns to apply to someone (a process that in itself is a conceptual model; there are languages with only one, non-gendered third person pronoun), you don’t ask for a karyotype test result or compared genitalia, but rather make the assumption from visible signifiers which don’t inherently match the biological sex.

The second one, social gender can be useful in examining social mechanisms and constructs, but in doing so creates a lot more edge cases. Now it isn’t just intersex and non-binary people that must be accounted for, but gender non-confirming people who, by definition, are edge cases in the model. The social model of gender becomes particularly dangerous, rather than simply incomplete to an alarming degree, when it becomes prescriptive instead of descriptive. To paraphrase a certain first century carpenter “The model was made for the people, the people were not made for the model”.

The final model, the individual model, essentially simply increases the resolution as high as it can go, and relies on people’s internal definition of gender. Full disclosure; I am agendered, so I don’t actually understand what it means to have a particular gender, but some people I know have very clear internal definitions. Some of these are based on physical sex or social norms; I think there’s quite a few cisgendered people who lack an internal definition like myself, but don’t have a reason to use a definition other than the biological one. We could call this being cis by default. Other definitions of gender are highly idiosyncratic, and to be honest I think this is inevitable just because, like I said above, the initial parameters that we are trying to model are really badly defined. What do we mean by gender? What weighting do we put onto different aspects of it? And that’s before we get into the question of working out the mechanisms that give rise to it; untangling biological and social influences is difficult enough given we can’t isolate and raise babies in a controlled lab because ethics is a thing and is important. As such, I think the best way to proceed is to find your own model, but acknowledge that it is not universal and accept other people’s own models of their gender. It’s unsatisfying, but at this point, what else can we do?

Hello Studyblr Community,

Just wanted to send out a little note - a friendly reminder - that if you have any troubles in a chemistry course or chemistry related topic feel free to send me a message. While my studyblr is here for personal motivation to finish up my undergrad, it’s also here as a resource for anyone who struggles or needs some simple help in chemistry. So far I have taken both general chemistries which cover topics ranging from unit conversions, titrations, ideal gas laws, molecular geometry, and intermolecular forces, *The list continues and I have multiple study/cheat sheets for many of these topics since my lecture was student-based teaching. Also, I have completed the first semester of organic chemistry that includes resonance structures, chirality, nomenclature, SN1/2 and E1/2 reactions, and alcohol synthesis. Right now I am enrolled in the second semester of organic chemistry (currently making a solid B in case you wanted to know how reliable I am with my knowledge) and have covered ether synthesis, aromatic nucleophilic/electrophilic substitution, activation/deactivation on the aromatic ring, amine synthesis, aldehyde/keytone synthesis, carboxylic synthesis. Next semester I will begin advance organic structure studies that include UV spectrum, proton and carbon 13 NMR, mass spectrum, and IR spectrum. Though I am already confident with handling those instruments and can help anyone who needs an understanding of how to label peaks or knowing what an unknown compound contains. On top of that, I will be taking analytical chemistry next semester as well. 

Of course, the list continues because I will always try my best to answer any chemistry related questions that my followers have. (Google does wonders for me and I have a good way of finding amazing study guides) So please don’t be shy when asking questions or correcting me when I’m wrong. I don’t have my degree yet in chemistry so I’m not always correct! :) Love you guys and keep up the good work. [Link to my ask box]

*It would be awesome if everyone could spread this little note so I can help anyone out who needs it. I hate to see students struggle in chemistry when I am currently on my way to becoming a teacher.  

Quantum Physics

Finding the expectation value

Cont’d from “Expectation value general form

The expectation value can be well understood by studying the mathematics applied to particular scenarios. In this post we will apply a quantum mechanic approach to find the expectation value of measurement.

Particle in a box example

Not to be confused with “Pressure of an ideal gas

This system is often known as the infinite square well.

Consider a particle with wavefunction in position representation given by

where N is a normalisation factor, confined to a 1-dimensional box in 0 ≤ x L.

We measure its momentum – what is the expected value of this measurement?

Thus, we need to find the expectation value of momentum in the x-direction;

since we can assume that the particle is entirely contained within the range 0 ≤ x L the limits can be adjusted to reflect this,

First, we’ll find the probability; |⟨ x | ψ ⟩|2:

and since we know that ⟨ ψ | x ⟩ = ⟨ x | ψ ⟩* we can find the complex conjugate of the given expression. So, we find that

which can be multiplied by the original expression to find

and since e0 = 1,

Now we must find px. Let’s look at the eigen-equation of its operator:

whose calculation provides the eigenvalue px. We know that this operator is given by

which we can act onto the wavefunction to get

for which we can calculate the derivative

and we know that

so

implying that

Thus, combining these factors into the expectation value equation, we get

and so,

Hopefully, the square well scenario will be examined in much more detail in future posts − including solving the Schrödinger equation for different scenarios.