Problem Solving Strategies - 2021-01-21

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Physics is my life

4:59 AM

Guys I am using frixion pens for my notes
With these pens , you can erase what you have written
but on YouTube and internet I found that if I keep my notes on the car dash or somewhere out where it is hot . My notes will be erased
If you know about these pens , then pls tell me if I should use these pens or not
I am preparing for jee

5:43 AM

@Physicsismylife this doesn't sound like a great idea to me.

Physics is my life

You know , it is very helpful but

@JohnRennie it didn’t happen with me

Just scared if it does

they also say if you put it back in freezer , the ink reappears

I've never used a frixion pen so I don't know how easy it is to erase them. I used a regular pen and if I made a mistake I just neatly crossed it out.

Physics is my life

Hmm k

what I am doing after writing all my notes

just rewrite them with regular pen

It takes like 3min max

But my notes are perfect in that case

@JohnRennie

No scribbling

That sounds fine, although if you were going to do that I'd just use a pencil, which is a lot cheaper than frixion pens.

2

Physics is my life

Ofc

Hmmm

that is better

I just didn’t knew earlier that frxion pens ink could be erased

5:53 AM

@Physicsismylife if you are preparing for JEE then i must suggest that you should focus more on your notes being concise and relevant, rather than them being "neat" and "looking nice"

2

Physics is my life

@satan29 ok.

@JohnRennie if you write sth with pencil , the written notes don’t vanish after 1 year also right

@satan29 I make my notes long

like 20 pages for a chapter

So , I make it in such a way that if I have to revise for boards

I dont need textbook

what do you think about that

user image

This is an example

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6:37 AM

Hello @JohnRennie sir

@PrateekMourya hi :-)

Sir are you free i mean are you answering another person?

I'm answering another question at the moment, but if you post your question I'll look at it as soon as I'm free.

Sir i like continuous conversation so ...

Please reping when you are free

Will do

6:54 AM

Sir i am going to coaching now i will try at night(india) or tomorrow

There should be a fixed time limit given to each user

Because sometimes its super annoying to wait that long

Also sometimes time for answering questions cant be predicted

OK

Who else agrees?

@PrateekMourya to be fair, if you had asked Satan29 he would have been happy to wait while I answered you.

3 hours later…

9:56 AM

Hey everyone, I have a preperation related qn, I usually feel very sleepy after lunch, and in the process drag out my work.(I want the time I get in afternoon) So what should I do to be able to concentrate in studies and not feel sleepy in afternoon?

<I sleep approx 7hrs a day> if you want to know that to answer. . .

also I just finished lunch. . . .

The usual way to address this is to eat a large breakfast, a medium size lunch and a small dinner.

@JohnRennie hi :-)

@napstablook hi :-)

do you follow that? How does that work?

I don't, but I eat a late lunch and for me lunch marks the end of my working day. So I don't care if I feel sleepy after lunch.

The idea is that you start with a large breakfast, and because you're fresh out of bed you still feel energetic.

Then at lunch time you don't feel that hungry because you had a large breakfast, so you only need a medium lunch, and because you haven't eaten a lot you don't feel as sleepy.

10:06 AM

@JohnRennie that makes a lot of sense, I will try to implement it hopefully to gain some few hrs everyday. thanks

Although I must ask what is the reason for decreasing order in dinner?

It's an old saying that dates back centuries.

Check this Google search

@JohnRennie Well there's no reason to not follow it :-))

3 hours later…

Physics is my life

1:02 PM

Yeah.Even I feel a lot sleepy

I sleep like 8hrs -9hrs a day

I will try your method

I don’t heavy breakfast but eat heavy lunch and dinner

Physics is my life

1:28 PM

Guys, why is the direction always along the line joining the two particles

Force should be there even if the line is big or small

I mean is that at centre of both the masses , force is highest

but it can be at the top of body to other Body’s top also right

2 hours later…

3:26 PM

@Physicsismylife If the force was not along the line there would be a net torque and angular momentum wouldn't be conserved.

@PrateekMourya ping me when you are free and I'll make time to answer your questions. I'll be eating lunch in a bit but I'll be free after 4 p.m. (9:30 p.m. Indian time).

3:47 PM

@JohnRennie Do you have time? I had a doubt in thermal radiation. . . .

@JohnRennie hello sir. :-) I want to ask something different. If you were to take an interview to test our understanding what questions would you ask?

@napstablook I'm about to start eating lunch. I'll be free in 15 minutes, but if Prateek is around he goes first as he's been waiting since this morning.

@Physicsismylife I make a lot of notes but I still use Textbooks during revisions, I guess I don't trust my past self to have written everything [even if I have written everything it's just me being paranoid]

@JohnRennie Definitely sir

4:12 PM

Hello @JohnRennie sir

@PrateekMourya hi :-)

Sir i was not angry with satan i thought its much better to know time when you are free

Neither of us realised you had to go to coaching so you didn't have much time.

No in particular for anyone

This way could really save time

Anyways

@JohnRennie sir please answer my question above this message

Starting here you mean?

yesterday, by Prateek Mourya

Inspired from this answer i made and explanation

4:17 PM

Yes sir

Give me a moment to read through it ...

Ok

@PrateekMourya when we derive the pressure for an ideal gas we tend to assume there is a single gas molecule bouncing between opposite faces of a box, then we multiply by the number of molecules in the box to get the total force.

Ok

But in reality this is not what happens. The mean free path of a gas molecule at atmospheric pressure and room temperature is about a micron i.e. the molecule only travels for a micron before colliding with another molecule and bouncing off in some random direction.

4:23 PM

Ok

The explanation was that the time delay on average is zero

So if you consider a molecule in the centre of the box it is never going to reach the edges of the box because it can only travel a micron before scattering off in some random direction. On average it will just stay close to the middle of the box.

And likewise, the molecules at the edge of the box stay close to the edge of the box.

user image

Ok

But all these collisions are elastic, and they happen so frequently that all the molecules share their energy and on average have the same speeds.

Let me draw a quick diagram to illustrate what I'm going to say. It'll take me a couple of minutes ...

Ok sir

4:30 PM

user image

@PrateekMourya The top diagram shows two molecules colliding and bouncing apart.

Ok

They are identical molecules, e.g. in hydrogen gas they would both be H₂ molecules, and I've just coloured them to show which is which.

But suppose the molecules were truly ideal, then they would pass straight through each other without colliding because ideal gases don't interact at all so their molecules cannot collide.

That's what I've shown in the lower diagram.

@PrateekMourya OK so far?

But collision are elastic

As the postulate of ideal gas

Yes, collisions are elastic. My diagram doesn't say they aren't ...

So collision do happen

@JohnRennie this point

I was asking that they do collide

4:34 PM

In real life collisions happen, in a truly ideal gas they wouldn't.

Or not?

So the postulate?

But the point I'm going to make is that in both cases we have two molecules coming in at speed v and the two molecules flying apart with speed v.

And remember that the molecules are identical so we can't tell which is which.

Ok

So if you just observed the two molecules going in, then observed the two molecules coming out, you couldn't tell if there had been a collision or not.

In both cases the in and out speeds are the same.

Ok

4:38 PM

So the point I am trying to make is that as far as the properties of the gas are concerned it doesn't matter whether the molecules collide or not.

If you took a snapshot of all the molecules of the gas, including measuring their speeds, then you could not tell from the snapshot whether the molecules were colliding or not.

So how can we still apply ideal gas equation to smaller sections?

Yes, you can do.

But what I was working round to saying is that the gas molecules stay in the open box because they keep colliding wth the gas moecules above them.

Ya since they aren't identical

Which I think is what you are saying. If you divide the gas up into layers of molecules, then each layer exerts a force on the layer above due to the collisions.

@JohnRennie yes

4:42 PM

In a closed box the top layer is in contact with the top edge of the box.

In an open box we in effect have a huge stack of layers of gas going up all the way to the edge of the atmosphere.

So each layer is supporting the weight of all the layers above it.

Ok

And this happens because the gas molecules collide so often. Since the mean free path is about a micron it's like we have layers of gas about a micron thick.

Ok

@PrateekMourya I've just found a diagram I drew when you first asked about collisions in the gas. Let me post it ...

user image

I'm not sure how well this works, but it's supposed to show the red molecule moving without colliding, while the blue molecules are colliding, but actually the end result is the same in both cases.

I wish i could tell you my mind stimulation

4:49 PM

With the collisions it still looks the same as a single molecule moving without colliding

I was imagining some Billiard balls on a table that are colliding with walls

That's a perfectly good model to use ...

And after collision with other molecules

They still collide the same way before

That what came to my mimd after watching the diagram

Yes. If you counted the collisions per second with the edges of the table you'd find they are the same as if the balls were not colliding with each other at all.

But still what i cant understand is when we account gravity

How do balance the weight

Of layer above them

4:53 PM

Consider the layer of gas next to the ground. Molecules heading down will hit the ground and bounce up again.

Yes

But when the molecules in the first layer head upwards they will collide with the molecules in the second layer that are moving down.

The collision will make the molecules bounce back and head down again, while the molecules in the second layer will bounce back and head up again.

So the molecules in the second layer are kept up by colliding with the molecules in the layer below them.

Just this time because of considerable length of conayanineer

Conatiner

Container

Slowy the effect of gravity makes the collision so that it effect is also Balanced

Simce even in the equation the graoh grows very slowly

There are two different things we need to consider:
1. why are the upper gas molecules kept up when gravity is trying to pull them down
2. why does the pressure gradually reduce when we go upwards

e^-mgh/rt

4:57 PM

What I've been talking about is (1) i.e. how the collisions in each layer support the layer above. Yes?

Yes

So we need to think about (2) as well.

Again imagine the gas divided up into horizontal layers.

In each layer gas molecules move up, collide with the layer above, then bounce back down again.

Then they move down, collide with the layer below, then bounce back up again.

OK so far?

Ol

Ok

But when a gas molecule is moving up it is slowing down because gravity is pulling it down. So when it reaches the top of its layer it has slowed down very slightly.

Likewise, when it is falling down it is accelerating because gravity is pulling it down. So when it reaches the bottom of its layer it has speeded up very slightly.

Ol

5:02 PM

OK so far?

Ok

Now i understand

And that means the collision with the layer below are slightly harder than the collisions with the layer above, because the collision speed is greater at the bottom of the layer than at the top of the layer. Yes?

Ok

I can continue from here

And that's why the pressure is very slightly greater at the bottom of the layer than at the top of the layer.

Ok

Thanks sir

5:04 PM

You're welcome :-)

Now I need to go and wash my plate and the pans.

Sorry for that time

This sort of thing is worth spending time on, because once you get it you'll remember it forever!

Bye sir

Have a nice day

Bye :-)

1 hour later…

6:22 PM

@JohnRennie Can u explain what I just posted

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Alsothere is a diagram attached to this

Please do have a look

2 hours later…

8:21 PM

Hello

I am jee aspirant

nice to meet you all

3 hours later…

11:20 PM

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Jan '2121

Problem Solving Strategies

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