ideal gas

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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!

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)

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

—–

Biology 

Chemistry

Anatomy & Physiology

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.  

The universe is expanding at an accelerating rate, or is it?

Five years ago, the Nobel Prize in Physics was awarded to three astronomers for their discovery, in the late 1990s, that the universe is expanding at an accelerating pace.

Their conclusions were based on analysis of Type Ia supernovae – the spectacular thermonuclear explosion of dying stars – picked up by the Hubble space telescope and large ground-based telescopes. It led to the widespread acceptance of the idea that the universe is dominated by a mysterious substance named ‘dark energy’ that drives this accelerating expansion.

Now, a team of scientists led by Professor Subir Sarkar of Oxford University’s Department of Physics has cast doubt on this standard cosmological concept. Making use of a vastly increased data set – a catalogue of 740 Type Ia supernovae, more than ten times the original sample size – the researchers have found that the evidence for acceleration may be flimsier than previously thought, with the data being consistent with a constant rate of expansion.

The study is published in the Nature journal Scientific Reports.

Keep reading

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.

I’m staring at my homework and scratching my nails against the wood of my desk because I am being asked about rate laws and reaction orders and homogenous catalysts and I don’t even know what the hell I am doing in this chemistry class because I really just want to write and the stress here is bumming me out and I can’t think when my mind is racing with a million other things. I am being asked about rates and all I can feel is the rate of my heartbeat increasing as the time is nearing 4 AM and I know I have to start getting ready for class in a little over two hours and I can feel the blood rushing to my brain trying to figure out these equations but I wasn’t meant for this– I wasn’t meant to play with chemicals and their abilities to react, man I don’t even know what makes me go, let alone a couple of beakers full of unknowns. These days it’s been hard to keep myself motivated and it’s bringing me down because when I see these numbers and names flash before my eyes, it just means that I’m losing time for the novel I had planned in my mind and I am miserable doing what I do now and following the path they are asking of me and God this doesn’t make me happy. Nothing seems to fall in line anymore– I can’t even organize my emails and I am losing who I am in the constant bombardment of classwork and homework and pressure, pressure, pressure, kind of like the type I see in the ideal-gas law, except in this life, pressure and volume are not inversely proportional because I have to make myself big enough to take on all the pressure: I have to cancel plans, I have to put aside health, I have to make room for all this pressure before I explode. And how horrible it is that the thought of that doesn’t even seem so bad anymore.
—  Falling behind in chemistry class
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The universe is expanding at an accelerating rate – or is it?

Five years ago, the Nobel Prize in Physics was awarded to three astronomers for their discovery, in the late 1990s, that the universe is expanding at an accelerating pace.

Their conclusions were based on analysis of Type Ia supernovae - the spectacular thermonuclear explosion of dying stars - picked up by the Hubble space telescope and large ground-based telescopes. It led to the widespread acceptance of the idea that the universe is dominated by a mysterious substance named ‘dark energy’ that drives this accelerating expansion.

Now, a team of scientists led by Professor Subir Sarkar of Oxford University’s Department of Physics has cast doubt on this standard cosmological concept. Making use of a vastly increased data set - a catalogue of 740 Type Ia supernovae, more than ten times the original sample size - the researchers have found that the evidence for acceleration may be flimsier than previously thought, with the data being consistent with a constant rate of expansion.

The study is published in the Nature journal Scientific Reports.
Professor Sarkar, who also holds a position at the Niels Bohr Institute in Copenhagen, said: 'The discovery of the accelerating expansion of the universe won the Nobel Prize, the Gruber Cosmology Prize, and the Breakthrough Prize in Fundamental Physics. It led to the widespread acceptance of the idea that the universe is dominated by “dark energy” that behaves like a cosmological constant - this is now the “standard model” of cosmology.

'However, there now exists a much bigger database of supernovae on which to perform rigorous and detailed statistical analyses. We analysed the latest catalogue of 740 Type Ia supernovae - over ten times bigger than the original samples on which the discovery claim was based - and found that the evidence for accelerated expansion is, at most, what physicists call “3 sigma”. This is far short of the “5 sigma” standard required to claim a discovery of fundamental significance.

'An analogous example in this context would be the recent suggestion for a new particle weighing 750 GeV based on data from the Large Hadron Collider at CERN. It initially had even higher significance - 3.9 and 3.4 sigma in December last year - and stimulated over 500 theoretical papers. However, it was announced in August that new data shows that the significance has dropped to less than 1 sigma. It was just a statistical fluctuation, and there is no such particle.’

There is other data available that appears to support the idea of an accelerating universe, such as information on the cosmic microwave background - the faint afterglow of the Big Bang - from the Planck satellite. However, Professor Sarkar said: 'All of these tests are indirect, carried out in the framework of an assumed model, and the cosmic microwave background is not directly affected by dark energy. Actually, there is indeed a subtle effect, the late-integrated Sachs-Wolfe effect, but this has not been convincingly detected.

'So it is quite possible that we are being misled and that the apparent manifestation of dark energy is a consequence of analysing the data in an oversimplified theoretical model - one that was in fact constructed in the 1930s, long before there was any real data. A more sophisticated theoretical framework accounting for the observation that the universe is not exactly homogeneous and that its matter content may not behave as an ideal gas - two key assumptions of standard cosmology - may well be able to account for all observations without requiring dark energy. Indeed, vacuum energy is something of which we have absolutely no understanding in fundamental theory.’

Professor Sarkar added: 'Naturally, a lot of work will be necessary to convince the physics community of this, but our work serves to demonstrate that a key pillar of the standard cosmological model is rather shaky. Hopefully this will motivate better analyses of cosmological data, as well as inspiring theorists to investigate more nuanced cosmological models.

Significant progress will be made when the European Extremely Large Telescope makes observations with an ultrasensitive “laser comb” to directly measure over a ten to 15-year period whether the expansion rate is indeed accelerating.’

Thermodynamics

Heat capacity

See previous posts about thermal physics

Heat capacity c is a measure of the amount of thermal energy Q can be put into a system before we see a change in its temperature ΔT. It is defined by the equation

where ΔT may be defined as ΔT = T - T0 for an initial temperature T0 and a final temperature T, so

Therefore, if you put 5 J of energy into some volume of liquid, we’ll call it X, which is at an initial temperature T0 = 20°C and observed its temperature change to T = 25°C then it would have a heat capacity cX

Specific heat capacity

This is particularly useful for engineering purposes because a heat capacity can be used to characterise gases and materials etc. For example, the specific heat capacity c of a material is found using its heat capacity per unit mass:

(note that this equation assumes that the heat capacity is independent of mass – i.e. for no phase transitions).

could you please ask your followers to click on the link/watch my final video project for chemistry and to give our video a thumbs up? the link is https://www.youtube.com/watch?v=-mC1wUoUMc8 . we get graded on how many views/likes we get, so I’d really appreciate it! :) thanks so much

So you guys should totally watch this chemistry video that raps about the ideal gas laws. :D

It helps out students, so that’s cool as well.