Analysis and String theory

Now it’s week 4 of teaching and my progress is bloody slow. It seems I could not speed up my learning. May be due to several reasons.

1. I always feel sleepy inside and outside the lecture halls. I always feel i lack of good sleeps.
2. The subjects are redundant. This sem light, matter and chemical change is equivalent to quantum mechanics and thermal physics last sem. So, I assume it should be easy, but actually it’s not. It’s really hard and tough subject.
3. May be bcoz I got excellent results last sem, I tend to be lazy and inconsistent. Astagfirullah, Oh Allah, please grant upon me the ability to move, to work, and to study.

2 lectures I often fall asleep, inorganic chem and light, matter and chemical change(LMCC). But not so far for analysis and maths methods. Those subjects really stimulate my nerve and adrenaline to rush. What to do, maths methods is tough, I need the give physical interpretation for the soln, and interpret the wordings into mathematical language. And the lecturer for maths method holds 2 major; in applied maths and inorganic and physical chemistry.

So far so good for analysis. The lecturer is so good that he’s very concerned about student. I just realize he tries to make joke in serious. I meant he is serious even though he’s making joke. He keep telling about the application of analysis in physics and engineering. Especially when describing about singularity and infinity.

Holomorphic and analytic function, as a function of z only, we don’t know where z bar is although we seem to know z bar just bcoz it’s the conjugate of z. But they are totally independent. He emphasize so much about holomorphic function and analyticity.

Aha..what to do. It’s bcoz he is a mathematical physicist and string theorist. So everything in mathematical analysis he gives interpretation in physics (string theory). But it’s good to have a string theorist/maths physicist as your lecturer. Bcoz it might be interesting to know the application plus some extra knowledge about universe and its extra dimension.

Ok, I got to go. Need to finish tutes for analysis, inorganic chem, physical chem as well as practical reports for physical and inorganic chem. So tedious and tired.

 

1st law of TMD (thermodyamics)

1st law of TMD; ΔU = q + w

Note I post this entry under chemistry, not physics nor both physics and chemistry. We’ll see the reason why. Different views hold by physicists and chemists.

In chemistry, ΔU = 0 for isothermal process when the KE and PE isn’t changing. Let’s see the eqn

H2O(l) -> H2O(g) at 100 C/373 K. Obviously the temperature is not changing. The phase change occur only at 373K for this pcs/rxn. Nevertheless the ΔU is not zero. Why? Bcoz the internal energy must change bcoz the pcs consume energy to break the intermolecular force, in this case in Hydrogen bonding, so that phase change can occur.

In chemists’ view, it makes sense. However when I refer back to knowledge in quantum mechanics and thermal physics, it’s totally paradox bcoz this pcs should give ΔU = 0. But I don’t refer to my lecture notes in physics yet. I don’t want to get confused and mix up chemistry and physics. Later on, when I get free time, I’ll post the entry from physicists’ view of 1st law TMD. So, I HOPE no one will comment about this internal energy change. I will immediately delete your comment if u do so.

Now ΔU = q + w , given the heat of vaporisation, ΔH(vap) = q , q is mechanism of energy transfer by heat to break the intermolecular bond. So, how about work,w? We still use the eqn w = -∫P dV . But ΔV = Vf-Vi. Here Vf = vol of H2O in gaseous form, Vi = vol of H2O in liquid form. Here we make successful assumption, Vf >> Vi, since vol of liquid H2O is negligible compared to vol of gaseous H2O. Thus w = -PVf. It makes sense bcoz the gas expands into gaseous form. So it loses energy in order to expand the volume(vol).

Aha..almost done. We got q = ΔH(vap) , we got w = -PVf, put back into 1st law of TMD. Then we’ll achieve ΔU. Note that ΔH(vap) can also referred as the enthalpy change, ΔH of system.

From definition, H = U + PV . Put into differential form, dH = dU + d(PV) = dU + PdV + VdP . Substitute the 1st of law of TMD, dU = dq + dw , here dw = - PdV. So our “1st law of TMD” is dU = dq - PdV. Substitute into dH = dU + PdV + VdP , it becomes dH = dq - PdV + PdV + VdP. Simplifying, dH = dq + VdP. But our rxn, H2O(l) -> H2O(g) occurs under atmosphere pressure (atm), so pressure is constant, dP = 0. Finally dH = dq. Integrating and putting limit we get ΔH = q.

In the next few entry, I will explain the difference of dH and ΔH, dU and ΔU. This is subtle difference of differential form and difference form. My friend got confused about this. So be patient and stay tuned.

 

Balancing redox reaction

Not even 1 year, I’ve forgotten how to balance the redox reaction (rxn). I did remember a bit when I was doing it in 1st year. Now in 2nd year semester 2, I don’t remember it clearly. How bad I’m; study for the sake of exam. Opss..I do study for the sake of knowledge to. I’m knowledge oriented rather than grade oriented.

Now, let’s balance the redox rxn.

In acidic solution (soln)

1. separate the redox rxn into reduction[red] and oxidation[ox]
2. Balance the number (#) of atoms besides oxygen and hydrogen, usually the metals.
3. Balance the # oxygen by adding water (H20).
4. Balance the # hydrogen by adding proton (H+).
5. Balance the charge by adding electron (e-).
6. Add up the rxn with the equal number of electrons in both [ox] and [red].
7. Simplify the eqn by cancelling common terms.

In basic soln

1. Add the equal amount of hydroxide (OH-) on both sides to compensate the # H+
2. H+ + OH-  -> H2O
3. Simplify the # H20 by subtracting the lower amount of H20.

Aha, we’re done. Good luck this semester.

 

Termodynamics in chemistry

The first 2 lectures we’re revising the 1st year stuff, the 1st law of thermodynamics (TMD), enthalpy, and work. Let’s see how it goes, how it differs from thermal physics in the semester 1.

1st law of TMD ΔU = q + w

q = heat transfered TO the system by surrounding.
w = work done BY the system on surrounding.

Heat -> mechanism of energy transfer when there is a temperature difference.

Loosely speaking, heat is not a function of temperature, bcoz we’ll see that heat can be transfered by means of work in isothermal process.

Work = - ∫ P dV

1) here, P refers to external pressure, so the -ve sign comes to show the work is done AGAINST the external pressure.
2) for constant pressure, it’s easy. But when P(ext) changes, do use substitution PV = nRT => P = nRT/V provided(p.v) the system is an ideal gas (allowed to assume ideal gas by lecturer/tutor).

* note, in older text book for physics and engineering work, w = ∫ P dV. This is not wrong however. But when the work is defined this way, the 1st law must be in Q = ΔU + W. So the internal energy is always the same.

* Luckily my lecturer accept both conventions, BUT it must be consistent, DON’T MIX UP.

Reversible(rev) process(pcs)
The system do compression/expansion ’slowly’ so that the equilibrium is always achieved. But reversible process tell u nothing about the path. We can have rev adiabatic pcs, rev isothermal pcs or rev isobaric pcs as well as rev isochoric pcs.

Irreversible pcs
The system will experience a constant external pressure (usually final pressure) of the system. To calculate volume change, use V = nRT/P (p.v under ideal gas condition). Then do the integral.

Hm.. it will be easier and better if I can show the diagram. But I lack the technical ability. I can’t add “image” to this post bcoz this blog does not accept [.doc] form. It only accept JPEG, JPG or whatever form the image is.

Anyone knows how to put the diagram especially in PDF and .doc form? Help me

 

Msg from Maths Department

To every student in Analysis 252 lecture, here are some msg from the lecturer

This is a straightforward and very doable course. To do very well, consider the following.

1. Read the lecture notes (available on this web site) ahead of the lectures, then attend the lectures and listen to the explanations provided. From experience, there is a strong (positive) correlation between attending the lectures and doing well in this course. In fact, the same applies to all other courses!

2. Following each lecture, learn the material in the lecture notes (and any extra material or examples provided in the lectures) “inside out”. Make sure that you understand and can reproduce all the statements made. Do that on a regular basis, following every lecture. Don’t lag or fall behind.

3. Solve all problems in the problem sheets. Make sure that you understand what you are doing by figuring out how the solution would change if the problem changes a bit. Go to the tutes and ask for help with anything that you were unable to do. You need to do work beforehand to make full use of the tutes.

4. Make sure that you can solve all problems in all relevant past exams (once the corresponding material is covered in class). Past exams are available in the Bailieu Library.

5. Think about the material. Try to “see the wood for the trees”, or, if you wish, “to see the bigger picture”. You will find that the course has very few (but deep) basic new ideas. Everything else in the course follows from these.

6. Have fun with the subject: Complex analysis (which is basically what we are doing in this course) is not only a foundational topic in mathematics, and an essential one in all sciences, but also a very, very elegant one. This is really beautiful mathematics.

Cheers,
Dr Omar Foda, Lecturer Analysis 252

 

Gibss Free Energy

In chemistry, Gibbs Free Energy is defined as ΔG = -nRT ln K. But in physics, the the definition is slightly different. G = H - TS. Taking the derivative on both sides, ΔG = ΔH - TΔS - SΔT. This equation will be very useful at constant temperature. Bcoz the term SΔT goes to zero. Now, u’re left with  ΔG = ΔH - TΔS. Nevertheless, to put in words, ΔG means the max non PV work that can be extract from a particular reaction (ie chemical rxn). rxn = reaction.

I didn’t remember how did we derive the equation (eqn) ΔG = -nRT ln K. The most crucial part is not the derivation of Gibbs Free Energy, but the consequences.

If ΔG < 0, the system (chemical rxn) is spontaneous at all temperature
If ΔG > 0, the system is non-spontaneous at all temperature
If ΔG = 0, the system is at equilibrium.

The calculate Gibbs free energy, one can use both equation,  ΔG = -nRT ln K or ΔG = ΔH - TΔS depending on given situation and given values. I’m still confuse why I could not correlate Gibss free energy and Hemholtz energy. It seems both of them work independently under the same condition.

Hmm..welcome Gibbs energy, Good bye Hemholtz energy. Hopefully I will never see Hemholtz again. But I’d be LUCKY if I know how to derive Gibbs free energy for both eqn. Anyone knows?

 

Welcome sem 2

The 2nd sem is coming in less than 1 week. It starts on 28 July. Anyway my appeals to take Analysis and Mathematical methods next sem are approved by maths department. Christine looks very supportive and encouraging when she looks at my results. She even printed the lecture notes on eigenvector and eigenvalue. Thanks a lot.

It seems that maths method is much harder than analysis. Probably I’ll encounter more difficulties in maths method than analysis. I don’t mind. Both subjects have their own privileges.  Analysis is fun bcoz it’s a self-teaching and self-learning subject. Where as maths method is essential for physical chemistry and quantum mechanics and as well as a prerequisite for applied partial differential equation.

Another sad new, I missed the 3rd July lecture; solid photonic crystal.

Ok, I’m at the age of work. So, let’s work harder this semester and have a good start.

sem 2

• Light, Matter & Chemical Change B
• Physical Chemistry Practical II
• Inorganic and Bio-inorganic Chemistry A
• Mathematical Methods
• Analysis

NB:  Maths method is required for the 3rd year subjects; Quantum Mechanics and Applied Partial Differential Equations (PDE)

I got a sudden change for inorganic chemistry. Somehow I think it’s better to take inorganic chem with practical work rather than theoretical part only. Bcoz chemistry is useless without pracs. Indeed, it’s the time to watch colourful solutions produced in the lab together with spectroscopy needed to identify the compound.

This sem will be more chaotic than sem 1. It’s overload. The theoretical and practical part for physical chem run from week 1 till week 12. Luckily, inorganic part only up to week 8. So I’m free from inorganic about 1 month. The maths subjects run as usual, 12 weeks per semester.

Cheers, verily, with hardships there is relief. Overload, so much burden. Excited

 

Why do we bother

While reading at http://www.cosmicvariance.com/, I noticed the entry at does God exist in a multiuniverse (What do u say). Here is the statement;

Anyone who reads the blog might be surprised to hear that I don’t want to give people advice about their religious beliefs — I do it all the time! But context is crucial. This is our blog, and we write about whatever we’re interested in, and nobody is forced to read it. Likewise, if I’m invited to speak or write specifically about the subject of religion, I’m happy to be perfectly honest about my views.

I definitely agree with this statement. Similar happen to my blog. I’m free to write anything, anything that I like, my religious belief, my camera, my chemicals or what so ever. Because this blog is mine. I got the right to do anything I want.

But somehow I have to be smart by not hurting others, especially when embracing with scientists. Now let’s see the next statement;

….He had stumbled across “Why (Almost All) Cosmologists Are Atheists,” and insisted that I tell everyone why….

Of course when dealing with atheists or antisemitic practitioners, religious beliefs is the controversial debate.

I too, must not hurt each other with my religious belief. If u wanna ask religion related stuff, go and ask the expert, priests, rabbi or syeikh. Don’t ask somebody that has little knowledge about it.It will lead to disastrous debate and might end up killing each other.

My religion belief advises me not to insult others. And I hold very tightly with my deen. The Only One, Allah Almighty.

1. Say: O disbelievers!
2. I worship not that which ye worship;
3. Nor worship ye that which I worship.
4. And I shall not worship that which ye worship.
5. Nor will ye worship that which I worship.
6. Unto you your religion, and unto me my religion.

Al-Kafirun 109

Now clarify your beliefs, don’t ask me. I already got mine.

 

Quantum dots: artificial atoms – Prof Paul Mulvaney

Back to school. Today’s lecture was very stimulating, but I remain confusing. Trapping electrons in nanoscale semiconductor particles leads to materials with remarkable new properties. Carefully tailored particles called quantum dots confine electrons so that they emit brilliant colours when stimulated by ultraviolet light. Making the particles for specific applications requires many ingenious tricks. But these quantum dots are finding many new applications wherever colours are needed including labelling biological molecules in living cells to trace biochemical reaction pathways.

I was partially sleeping, may be a bit tired from playing soccer yesterday. But the demonstrations were wonderful. Why? Bcoz quantum dots produce many colorful crystal based on their sizes. 2-6 nm, ranging from blue to red. Prof Paul explained lots of quantum mechanics going on in the production of various colors. Basically depending on the energy levels of the treating like particle in the box in 3D quantum dots.  Aha.. I understand the quantum mechanics but not the procedure of how they cut the crystal in nano-size.

One of the significance in biology/medicine is that, when we inject quantum dots in the person having tumor (in the slideshow  he used rat), physicians are able to locate the tumor and how big it’s. Surgeons and doctors commonly have problem of estimating the size of the tumor, but using quantum dots is an advantage. However, the negativeness is that it might induce another tumor depending on precursors. If it has cadmium, selenium,  zinc sulfide it will be find. But if it contains arsenic..! (u tell me what’s the consequence).

Ok, got to sleep early again bcoz I have snow trip to Mt. Buller tomorrow morning. Can’t wait to eat the snow.

For next week Friday lecture is Solid Light: trapping photons in photonic crystals.

 

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