silver hair

I've known about ISIS and the wars fought by our brave brothers and sisters in the middle east - everything including what the US and Russia have done to be a part of this terrible thing. But I guess seeing the world distraught - no matter how deep (or shallow) their understanding may be in the situation- was indeed a breaking point for me.

Dear You,

 Yes, you. Even you who only had that spark of belief that maybe, just maybe. Even you who thought that I could be capable of so much more the first time you saw me, and slowly lost that belief somehow. Yes, you who thought of me, and what I could do, no matter how small, no matter if that is still true, even if it has faded away.

Most people say thank you last and maybe it’s nicer that way, to leave the reader a pleasant experience. I think it’s misleading. So like the calm before the storm, thank you. Thank you for believing in me, for thinking about me, for that hope you’ve shown, no matter how little. It doesn’t even matter if you said it, or if you just kept it in the back of your mind, or if you’ve forgotten. Thank you for believing in me. Thank you because somehow, I’ve thought of you, in a way, indirectly, or directly, whispering to myself in times I could not pick myself up, that somebody believes, and that somebody is you. So, thank you. Maybe you can understand how I feel, maybe this has happened to you, nevertheless, the gratitude I feel is immense.

Thank you for believing in me.

For the times that I’ve forgotten how capable I am, and about everything I have ever achieved, you were there to help me realize what I could do. For the times that I felt like pushing myself back because who am I, really, to lead this project, to undertake this mission, you were there to encourage me to at least try. You believed in me.

Thank you for believing in me.

And yet, there’s something missing.

Not words, nor hugs, not songs, nor smiles, not even money or rewards. What was missing was myself and everything I left behind when I detached myself from reality. I can no longer feel, I can no longer understand how it feels to believe. I know you want me to try but I never did, did I? I know you want me to succeed, but I know I never can. I know, in the back of your mind, somewhere, that you knew I could, but I never did. So eventually, you lost faith in me, you lost belief. Maybe you didn’t really, but you’ve forgotten what it’s like to watch me accomplish something. I’ve forgotten. I’ve sunken deep into my own pity and misery I think it’s too late to climb back up. No encouragements will help me get through this.

How can I pick myself up with your words and your thoughts? They never mattered. They stopped mattering when I refused to pick myself up. I’m sorry, I’ve failed you.

This should have been entitled, “An Open Letter to the Ones I’ve Disappointed” because everyone who has ever believed in me has been left disappointed.

But don’t worry, you can forget about me. No explanations needed. If you choose to leave, I will understand. I promise. I’ve understood.

You can rub this off as insignificant, rub this off like you didn’t read anything. Actually, I’d very much like you to forget about me and everything I could do. Let me be. I am responsible for my own doing. So forget about believing in me. It’s destructive. It’s broken both me and my confidence, both you and your trust. Forget. It’s such a bitter word, but it feels better after.

Lastly, I can make no more promises. I will not promise to better myself. I think I am way past that point. I can make no promises to fulfill your beliefs of me, of my capabilities, and of achieving something. I make no promises to lighten your heart. I make no promises to leave you happy. I cannot make these promises for I see no point in saying them, and believing I’ll actually do them. I cannot see the future, and I cannot guarantee what I’ll do.

U = TS - PV +  μN (Euler Form) [Derived from taking the partial derivative of U (S,V,N) with respect to a constant, λ]

taking the derivative of U using partial derivatives, we get:

dU = (TdS + SdT) - (PdV + VdP) + (μdN + Ndμ)

we subtract from this the equation dU = TdS - PdV + μdN

we get: 0 = SdT - VdP + Ndμ

rewriting,

dμ = -sdT + vdP [Gibbs-Duhem Relation)

where: s = S/N ; v = V/N

dμ = μ(T,P)

Notes:

U - Internal Energy

-extensive property (depends on the scale/size of system)

U is a function of S,V, and N.

where:

S-entropy

V-volume

N-number of moles

Internal Energy is path independent, it is a first-order homogeneous function (extensive), and it passes Euler’s test.

Given that U = U (S,V,N),

(δU/ δS) = T ; (δU/δV) = -P ; (δU/δN) = μ

1) Differentials/Derivatives - change in function with respect to its independent variables.

Definitions of terms:

a) Change in function - present state of a system to a new state

b) Function - property/state

c) Independent - (e.g. time)

2) Slope - tells what the state of a point is

3) Physical significance:

---Extremum Principle: tells the direction of the slope (inc/dec). When slope=0, the system is at its optimum point (max/min).

In order to determine if a system is in equilibrium, we have to know the state of the system both before and after, hence, the need for differentials.

Exact differential - pathway independent. This means that we are not concerned with the path the system takes in order to get from its present state to its new state. (i.e. we only need to know the state of the system before and after)

-determined by Euler’s test**

Euler’s test**

for a function f(x,y), if:

δ/ δy [ δf/ δx] =  δ/ δx [ δf/ δy]

then the function is exact.

[The notation above only means that if we take the partial derivative of f with respect to x and take that [1]derivative’s partial derivative with respect to y, and then take the partial derivative of the same function f with respect to y and then take that [2]derivative’s partial derivative with respect to x, they should be equal]

[For more information on the test of exactness, read up on: http://www.chem.arizona.edu/~salzmanr/480a/480ants/e&idiff/e&idiff.html]

For example, if we were to measure the work of the system, we would notice that work is an inexact differential since the path matters. To explain this, we take the scenario of a car moving downhill. If the car goes straight down, without stepping on the brakes, whatever is below the hill will have a large amount of work exerted on it. However, if the car steps on the break does a large amount of work (i.e. the breaks), then that thing that is below the hill would not have that large amount of work exerted on it because the car took the blow (i.e. the work was placed on the car instead of the thing on the bottom of the hill).