@JohnRennie Sir I have a problem particularly with regard to a lead zinc system

@user586228 hi :-)

For any system

Even let us say

Si(pure,l)=Si(1 wt % standard state in molten iron)

Ok..?

we are to calculate delta G m for silicon

In order to proove thhis

they calculated activity as p/p nought

I do not understand whether this is Raoultian or Henrian activity?

That sounds like the trick in Henry's law when you take the standard state that isn't the pure solute.

Could not get you

Can you slightly elaborate@JohnRennie

I'm currently doing another question so I'll be busy for a while.

I am not in a hurry..

Take your time :-)

@JohnRennie Can we speak once?

@JohnRennie hi, do you have time for a question right now?

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

sure, thanks

when we talk about heating up a disk with a hole in it, the hole expands in size just as the disk expands.

A fairly common explanation is to hypothetically imagine the expansion of the whole disk as if the hole did not exist, and then to argue that the same would happen with the hole, and thus the hole expands.

I've found this explanation multiple times online, but no solid explanation as to why the same thing happens with the hole. I'm looking for an explanation as to why this occurs; the more I've thought about it, the less obvious it seems to me. For example, let us consider two cases:

Let's take a rectangular plate, and cut a hole in it; the hole increases in size.

Now if we make the hole so big that it basically divides the plate into two parts, the hole obviously doesn't expand anymore.

However, if we make the hole just big enough that a thin rod stays between the two new plates on the left and right, according to the common explanation that hole should still expand since we can consider the expansion that would have occurred if the hole never existed. But does this mean that this thin rod is under a big load of tension now? Since if we just make the hole slightly bigger to split the plate into two pieces, the plates expand in the opposite direction.

@AshishAhuja in this case we basically have two separate plates which expand towards each other and the gap between then becomes smaller, not bigger, that's what I mean.

I think that explains my question, I can draw a diagram if needed; I'm basically free the whole day today, so please just ping me whenever you're free.

@AshishAhuja yeah I was searching for sometime for some kind of a proof

to me when attacking this situation from what ive seen in real life, it feels like the hole gets smaller too

@AshishAhuja it becomes bigger actually

@RishiNandhaVanchi no, how? If we have two separate plates at a certain distance from each other, won't they expand towards each other making the gap smaller?

distance between every single spot in the object increments

by the same amount

they aren't part of the same object.. ?

As in we split up the plate into two parts

a result of that distance increasing between everyspot makes the object just a scaled version of themselves

it maybe counterintuitive

uhhh I'm talking about something else, give me a second to explain..

I think i get what you are saying

wait actually I'll draw a diagram quick..

with two seperate objects the gap decreases because they get bigger right?

isnt that what you are saying

yes, one part of it.

(one part of what I'm saying)

the next part is?

that's actually the second part. Just give me a moment please, I'll draw a few diagrams..

that's the original disk...

lets say the hole is a circle, so part of it that belonds to each one is a semicircle. You are saying the semi-circle will get squished and less concave because of expansion right?

That's the plate after we cut a massive hole in it; according to the general explanation, the hole should still expand

yeah

the small portion in between expands too

oh okay i get it now

now its becomes a thing about how the positions of the two pieces are held

Now if we make the hole just a bit bigger, the expansion takes place in the opposite way; so does that mean that the thin rod was under a lot of tension?

yes I got what you'r saying

@RishiNandhaVanchi sorry, I don't understand...

ill try my best

@AshishAhuja you're saying that if we heat this:

take the original object. lets call the centre piece C and the two rectangles L and R

The hole doesn't expand?

uhhh...

originally C forces L and R to move away form each other on expansion (so like centres of L and R move away)

but now that constraint isnt there

@JohnRennie it should I guess, now that I see it from this perspective.. but what about the two plates? In that case it seems to me like the hole shouldn't expand, since the two plates will just become bigger independently.

in the circle case the semicircle radii get larger but seperation between two ends become smaller (because centres arent contraint to move away from each other now)

@AshishAhuja yes, that's true, but even when the two sides are completely disconnected we can define a radius of curvature for the curved edge. Yes?

@RishiNandhaVanchi hmm, I guess I'm talking about the case when they aren't held together..

@JohnRennie yup

And as we heat the disconnected plates that radius of curvature increases. Yes?

I agree intuitively on that part, but I do not know of a formal proof for that. Let's just take that as a yes for now.

Since the two parts are disconnected you can put them at any distance from each other that you want, but let's suppose we put then at the right distance for the two curved edges to be arcs of the same circle. This just means the distance between the two midpoints of the curved edges is equal to twice the radius of curvature.

e@JohnRennie Can we discuss about the Henry's law problem.

@AshishAhuja like that?

yes

Then this circle is effectively the "hole in the plate" even though the hole is actually bigger than the plate is. Yes?

ahh yes

So that's what we mean when we say the hole expands at the same rate the plate expands even in this case when the hole is bigger than the plate.

We are just defining the hole in terms of the radius of curvature of the two (disconnected) curved edges.

@AshishAhuja Is there something similar to LaTeX for schematic such as this?

@JohnRennie and this?

@RishiNandhaVanchi I use Google Draw

It's free and works very well for simple diagrams like this.

ohok sir

I thought it was coded

like LaTeX

That would be faaaaaaaaaaaaar too much work! :-)

@JohnRennie makes complete sense, but what if the two plates were not at a distance of 2 * r? Then the effective gap does become smaller right?

I just draw the diagram in Google Draw then screen shot it, paste in MS Paint, save it as a gif and upload it here.

@RishiNandhaVanchi I used Google Draw too

@AshishAhuja yes, but if the plates are disconnected you can move them around ny way you want.

I guess you could say we put the plates on a frictionless surface so their COM stays constant as they expand.

In that case the distance between them would indeed get smaller as they expanded.

so if their distance become smaller, isn't that contradicting the radius of curvature explanation?

@JohnRennie weren't we talking about a plate on a frictionless surface all this time?

@JohnRennie can you share the software where you drew these

@AshishAhuja No, because we define the radius of the hole to be the radius of curvature of the curved edges, not half the distance between the plates.

@user586228 Google Draw

btw can we get back to henry?

ahh ok I get it now.

after this

@JohnRennie

@AshishAhuja I didn't see the start of the discussion, but yes it makes sense to imagine this happening on a frictionless surface.

@satan29 haha yes. People who put a lot of effort into neatness but miss out on content tell me "My notes are beautiful looking. but that's about it". but that isnt to say you should make your notes look as bad as mine tho XD

@user586228 I didn't understand your question. I would have to see what your book said.

@JohnRennie I am asking about this

@JohnRennie yeah I didn't mention frictionless surface but I thought it was implied. Otherwise it would probably become too complicated to analyze, wouldn't it?

@AshishAhuja yes, I'm not sure how you would do it if you have to include friction. In general the COM would move I think.

@user586228 didn't we talk about this before?

@RishiNandhaVanchi btw this proof along with the radius of curvature explanation above seems to clear it up for me, in a formal way.

No we didn't

It was that discussion.

@JohnRennie that clears it up for me, thank you.

@AshishAhuja :-)

hmmm

@JohnRennie I could not get it

Which exception are you talking about please explain in a vivid manner.

It's another of the weird tricks that engineers use, and I don't know enough about it to explain it.

Please tell me whatever you know

@JohnRennie you clearly explained something

I mean hinted at something

That's going to be a long discussion and I don't want to do that at the moment.

Actually I have exam very soon

Please give me a slight hint

@JohnRennie This is a request

Lets say I wish to solve this differential equation.

What is difficult while solving this differential equation is that..

It is very diffcult for me to get the intergration constant while I integrate it for the first time.

I intend to use definite integral with proper limits the next time...So integration constants is never a botheration..

@JohnRennie hi

@user586228 what's difficult? if the derivative is zero then the function is constant...

True but tell me something how I get the limit for that?