Problem Solving Strategies

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user8718165

7:06 AM

Good morning Sir :) @JohnRennie

John Rennie

@user8718165 morning. I'm afraid I'm going to be working for the hour or two. Sorry :-(

Kevin N

@JohnRennie I was trying to view an old message, about a week ago but mathjax won't work there. Any solution?

$$ \psi = \int_{x=0}^{x=a} \psi(x) dx $$

This was the equation, but only the codex are there. It seems Mathjax doesn't function on older messages

yuvraj singh

@JohnRennie hi.

user8718165

@JohnRennie It's okay sir...No worries 😊

2 hours later…

Kevin N

8:58 AM

@JohnRennie

I posted this question a week or two ago. You said:

Are you also assuming that: $\theta_2 ⩽ pi/6$

2 hours later…

user8718165

11:29 AM

Hello sir @JohnRennie

@JohnRennie Sir I want to ask you some questions... are you free now? :)

John Rennie

@user8718165 I'm helping with Aladdin's Python coding I'm afraid. You can ask but I might be slow to reply.

user8718165

@JohnRennie okay Sir....how long will you be there?

@JohnRennie Will you return in the evening sir?

John Rennie

I am here for about an hour i.e. until 12:30 UK time. After that I won't be back util tomorrow.

user8718165

@JohnRennie okay Sir... You please ping me when user Aladdin is done. Please Sir

John Rennie

@user8718165 will do :-)

user8718165

11:45 AM

@JohnRennie thank you so much sir

John Rennie

12:09 PM

@user8718165 i think Aladdin and I are nearly done. Do you want to ask now as I'm going in 20 minutes.

user8718165

@JohnRennie hello sir...yes...cooking an egg is endothermic and increases its entropy...I got the reason but why sir...?Shouldn't entropy be decreased like if we consider the case of a piston system?

@JohnRennie also when we pull a rubber band, its entropy is decreased....but the rubber band will heat up a little...so shouldn't it increase?

John Rennie

If you consider the egg as a system, then for a reversible process the entropy change of the egg when some heat $dQ$ is added is given by $dS = dQ/T$.

user8718165

@JohnRennie okay sir...

John Rennie

We add heat to the egg when we boil it, so we would expect the entropy of the egg to increase. Yes?

user8718165

@JohnRennie yes sir...actually that equation was also one of my problems....well...continue :)

John Rennie

12:19 PM

Why do you think the entropy of the egg should decrease?

The volume of the egg isn't changing ...

user8718165

@JohnRennie okay sir...got it...what about a rubber band sir?

John Rennie

With the rubber band we are not adding any heat to the system. We just stretch the band.

user8718165

@JohnRennie okay sir....

@JohnRennie sir...it heats up the band...does it?

John Rennie

When we stretch the band it tends to make the molecules line up, and that reduces the randomness of the molecules so it reduces the entropy.

But assuming this is a reversible process, we aren't adding or removing any heat so $dQ=0$ and that implies $dS=0$.

But the entropy due to the shape of the molecules is decreasing so it looks as if entropy is going down.

user8718165

@JohnRennie yeah sir...got that reason...but won't it heat up by itself if we stretch it?

@JohnRennie okay sir

John Rennie

12:25 PM

So what happens is that the band heats up and that raises the entropy again. The entropy increase due to temperature rise exactly balances the entropy decrease due the shape of the molecules so the total entropy change is zero.

Note that no heat is being added or removed. What happens is that the internal energy of the rubber is redistributed.

user8718165

@JohnRennie okay sir...so change in entropy is 0 right?

John Rennie

@user8718165 Correct.

There is no change in the total entropy of the rubber band.

user8718165

@JohnRennie I was puzzled. It's written that entropy decreased...well okay:)

John Rennie

Entropy in a material can have several different sources.

There is entropy associated with the temperature, and there is entropy associated with the configuration of the molecules in the rubber.

user8718165

@JohnRennie okay sir...like heat, molecular arrangement..right?

John Rennie

12:27 PM

@user8718165 yes

user8718165

@JohnRennie okay...sir...one more qn

John Rennie

In effect, by stretching the band you are redistributing the entropy inside it.

user8718165

@JohnRennie yeah sir...got it

John Rennie

What's the one more qn? Make it quick!

You have two minutes :-)

user8718165

@JohnRennie Sir Kelvin-Planck states that this is not possible...why sir

@JohnRennie I'm trying to do it ASAP :(

John Rennie

12:29 PM

You mean why can't an engine be 100% efficient i.e. convert all the heat that flows from the hot source to work?

user8718165

It says there is a cold reservoir needed always for heat rejection

@JohnRennie yeah sir...atlest in ideal case

John Rennie

I'll have to think about that. As I recall the argument is that if that were possible you could hook the heat engine up to a heat pump and get a free energy i.e. create energy from nothing.

But I can't remember the detail.

user8718165

@JohnRennie okay sir...just one last qn

@JohnRennie no worries

John Rennie

I'm sure you could Google it. Try maximum efficiency of reversible engine or something like that.

Carnot's theorem (thermodynamics)

Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also called Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain. The efficiency of a Carnot engine depends solely on the temperatures of the hot and cold reservoirs. Carnot's theorem states that all heat engines between two heat reservoirs are less efficient than a Carnot heat engine operating between the same reservoirs. Every Carnot heat engine between a pair of heat reservoirs is equally efficient, regardless of the working substance employed or the operation details. The...

There you go, that explains it.

user8718165

@JohnRennie okay sir $dS = dQ/T$ why not $dS = dQ/dT$?

John Rennie

12:33 PM

> Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain

@user8718165 Because $dQ/dT$ is the specific heat.

user8718165

@JohnRennie yeah sir...I was thinking about it...how just removing a d changes the definition? I'm not getting it....Is there a proof?

John Rennie

I'm sure there's a proof somewhere but I don't know it.

user8718165