Problem Solving Strategies

user586228

2:55 AM

user586228

3:33 AM

user586228

4:10 AM

user586228

6:02 AM

@JohnRennie Sir r u there?

John Rennie

6:12 AM

@user586228 hi :-)

user586228

Hello:-)

Can you touch upon the first problem

John Rennie

I can't help with the first problem.

user586228

Ok no problem

Can you help with the last?

John Rennie

The second problem is presumably related to the rate of heat conduction from the metal sphere to the air. I can see in principle how to do it, but it looks a hard calculation. I'd guess engineers have a simplied equation for doing it.

The last question is easy because you just have to calculate the volume per iron atom.

user586228

Can u targent the third first

Ok

Why not the entire cell?

John Rennie

6:18 AM

The FCC unit cell contains four atoms while the BCC cell contains two atoms.

user586228

ok

So the total volume

should remain unaffected ..Isn;t it?

John Rennie

In the BCC phase the cell is 0.293nm and it contains two atoms, so the volume per atom is 0.293³/2 = 0.0126nm³

user586228

ok

John Rennie

In the FCC phase the volume per atom is 0.363³/4 = 0.0120nm³

user586228

ok

Now which minus which?

John Rennie

6:23 AM

So the percentage volume change is (Vf - Vi)/Vi = (0.0120 - 0.0126)/0.0126 = -4.9%

user586228

Answer is right

Now please tell me the phenomenon that occurs

How would the volume per atom change

Explain the mechanism slightly please..

John Rennie

There isn't a simple answer to that. It happens because the length of the Fe-Fe bond changes slightly when the phase changes.

user586228

Why did you not target the who cell

Why per atom

Please explain this to me.

John Rennie

Because if you have a lump of iron it has a constant number of atoms in it

user586228

ok

So...I still do not understand

John Rennie

6:27 AM

The total volume of the lump of iron is the number of atoms (which is constant) times the volume per atom.

So it's the volume per atom that we need to know.

user586228

Kind a because you do not know the totalatoms..??

Is it??

Or am I incorrect

Like dividing to have an intensive quantity?

True??

John Rennie

It only asks for the percentage change.

user586228

Ok...Is my observation correct?

John Rennie

If there are N atoms and the volume per atom is v, then Vi = Nvi and Vf = Nvf

The percentage change is (Vf - Vi)/Vi = (Nvf - Nvi)/Nvi and the N's cancel so we get (vf - vi)/vi

So we can just calculate the percentage change in the volume per atom.

user586228

How are you so sure that the N's are same

Please explain

It could be different for BCC and FCC also after the phase change

Why are they same?

John Rennie

6:33 AM

It's just a lump of iron. How can the number of atoms change when you heat or cool it?

user586228

Ok got you mole balanced

Now problem 2..Please get back to this one..

John Rennie

There will be some quick method engineers do for this. Trying to do it from first principles would be a complicated integral that I can't do.

user586228

@JohnRennie I have ample time

I do not regret if yo derive it from

First principles

user586228

6:54 AM

@JohnRennie Sir atleast tell the thinking process for the second problem if possible .I will figure out the rest myself.

John Rennie

@user586228 at some time t you have a liquid drop of radius r(t) that is less than the radius of the drop R, so there is a shell of solid iron of thickness R-r(t) around the liquid core.

The liquid is at 900K and the outer surface of the shell is at 300K (because it's cooled by the gas) so you have a temperature gradient of 600K across the shell.

From this you can calculate the rate of heat flow, dq/dt, and rate of solidification is the rate of heat flow divided by the latent heat of fusion.

And from the rate of solidification you can calculate the rate of decrease of the radius of the liquid core.

user586228

2:31 PM

@JohnRennie Sir this is what I have been told about the problem.

Always start with

In - Out + Generation = Accumulation

Out = Area*h*(T-Tair)*t
Gen = V*density*Hfusion
Somebody told me this
Even then I am not getting the answer
Any help in the direction is welcome

@JohnRennie Sir I need it soon tbh :-)

Prateek Mourya

4:52 PM

Hello @JohnRennie sir

John Rennie

@PrateekMourya hi :-)

Prateek Mourya

Sir a spring connected to a piston which is over a ideal gas

Initially the spring relaxed

The temperature is increased slowly

When spring stretched by x

Find work by gas

Sir here at every instance

How can we assume paiton to remain equilibrium

Piston

John Rennie

Let me draw a diagram ...

Prateek Mourya

Ya big fan of your diagrams

John Rennie

This is what I think it means.

Prateek Mourya

4:59 PM

Yes

John Rennie

The gas starts out at 1 atm and the spring is at its natural length. Then we heat the gas and the pressure goes up, so it exerts a force on the spring and compresses the spring.

Prateek Mourya

Yes

John Rennie

There is an easy way to calculate the work done, since the work done is the work done on the spring i.e. the work done is the change in PE is the spring ½kx²

Prateek Mourya

Yes but why piston remains equilibrium

John Rennie

Why would it not remain in equilibrium?

Prateek Mourya

5:03 PM

Because we don't know nature of increasing force

What increases in which way

Why would gas force increase such that spring force too increase same way

John Rennie

You mean if it expanded fast the expansion would be irreversible?

Prateek Mourya

Know suddenly one of force would increase much more than other

And cause u equilibrium

John Rennie

OK, suppose the piston has moved a distance x, then the tension in the spring is F = kx. Yes?

Prateek Mourya

Yes

Is it us who increase temperature such a way that piston remains equilibrium

John Rennie

The force on the piston due to the pressure in the gas is F = PA, where A is the area of the piston.

And for the system to be in equilibrium this force has to be the same as the tension in the spring. So we must have PA = kx.

Prateek Mourya

5:07 PM

Why this force has to same

I mean it doesn't increase

Such way that it balance spring force

When we released ablock connect to spring gravity would pull it

It would oscillate

John Rennie

The cylinder is heated, so the pressure increases. That's why the pressure goes up and balances out the spring tension.

Prateek Mourya

Will it every time increase in such a way that its forces exactly to the spring force

John Rennie

We start with no pressure in the piston and no tension in the spring so everything is in equilibrium. Yes?

Prateek Mourya

Yea

John Rennie

Then we slowly heat the piston.

Prateek Mourya

5:11 PM

Ok

John Rennie

As the temperature increases the pressure increases and it exerts an increased force on the piston. That pushes the piston out until the force due to the spring compression balances the force due to the increased pressure.

Prateek Mourya

Yes

More the force more compression

Since spring opposes it change in length

John Rennie

Yes

Prateek Mourya

But its not relatable to the spring gravity system

Where the force of gravity continuosly pull

John Rennie

I don't see why gravity is involved here ...

Prateek Mourya

5:16 PM

In some cases

Spring force is not always balanced

John Rennie

I think we would need to consider a specific question to go any further with this.

Prateek Mourya

A block attached to spring is released

Find maximum velocity of block

John Rennie

Can you post a picture of the question?

Prateek Mourya

I would need 5 mins

To go to my workplace

Its bit far away

Can you wait sir?

John Rennie

The trouble is that you are posting very vague questions with no details.

If you want to go and get your book or whatever so you can post the actual question then I'm willing to wait.

Prateek Mourya

5:30 PM

Block is released under gravity

Here spring force is not in equilibrium

Every time

John Rennie

OK. The spring starts at its natural length so the tension in the spring is zero.
When you let go of the block it accelerates downwards until the spring tension is equal to mg.
At this moment the net force on the block is zero and the block has reached its maximum velocity.
Then as the block continues moving downwards the spring tension is greater than mg so the net force is upwards and the block graually slows to a halt.
Then when the block has slowed to a halt it starts accelerating upwards agaon.

@PrateekMourya OK so far?

Prateek Mourya

Ok

Y
es exactly

Why doesn't this happen in case of the piston arrangement

Earlier

The pressure increases so the spring compress till it balance pressure force

But since piston gains velocity

It stretches more

John Rennie

I assume the piston and spring are on their side on a smooth surface.

Though I'd need to see exactly what the question said to be sure.