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  1. O

    Entropy of isothermal process reversible\irreversible

    We were shown in class how to get those entropys. For reversible isothermal - ΔT=0 thus ΔE=0 thus Q = -W. ΔS(sys) = Qrev/T = nR(V1/V2) And ΔS(surr) = -nR(V1/V2) because surroundings made opposite work. For irreversible isothermal in vacuum - ΔT=0 thus ΔE=0. No work is done by...
  2. O

    A simple question in thermodynamics

    But on both processes I start with same Pi and Vi, and end up with same Pf and Vf. I thought E is a state function, so it should not matter how I reached from initial to final state. If it's an ideal gas, then for same P and V I must get same T, regardless of any bath... What am I missing?
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    A simple question in thermodynamics

    I'm sure there are more than two ways, but I'm asking about these two. First is to relase the piston at once (getting a new constant external pressure). Second is to release it in very small steps (thus temprature remains constant). As far as I see we have the same Ef and Ei, because it should...
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    A simple question in thermodynamics

    I have a cylinder with gas in it. I can make it expand in two ways: spontaneously isobaric process or reversible isothermal process. I understand W and Q for each process are different, but is ΔE the same? If not - why?
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    Name the following molecule (common name and IUPAC)?

    I would need to know iso, sec and tert for my exam.. Some answers you should pick appear as iso\sec\tert rather than IUPAC formal names.. I wish it wasn't like that
  6. O

    Name the following molecule (common name and IUPAC)?

    Why not? Here is sec-butylcyclohexane: And another carbon to the chain simply makes it pentyl, am I wrong?
  7. O

    Name the following molecule (common name and IUPAC)?

    any iso/sec/tert name for it?
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    Name the following molecule (common name and IUPAC)?

    http://img43.imageshack.us/img43/2916/95953925.jpg [Broken] I understand molecule #1 is sec-pentylcyclohexane But how would you call molecule 2? Please give common and IUPAC names (no need for too much detailed explainations) Thank you.
  9. O

    Discrete math - simple formalism question

    Hi gustav Thanks for your reply Could you just explain what "s.t." means? I'm not very familiar with the english terms. Thanks a bunch
  10. O

    Discrete math - simple formalism question

    I never used descrete math terms in english before, so I hope it sounds clear enough: Formalize the following: 1) Between every two different real numbers there is a rational number 2) There exist real numbers x and y, such that x is smaller than y, yet x^2 is bigger than y^2 Now the solution...
  11. O

    Linear Algebra - Jordan form basis

    OK, please discard all of my question, I'm an idiot :) Everything is clear now, I thank you very much for the last time :)
  12. O

    Linear Algebra - Jordan form basis

    Oh ok, I discard my 3rd question... The answer is that I pick v2 to be \begin{pmatrix} 1 \\ -1 \\ 1 \\ -1 \end{pmatrix} Now I remain only with questions 1, and 2.. More related to equations system rather than J form I suppose
  13. O

    Linear Algebra - Jordan form basis

    Hmm, ok I see what you say.. So now I have 3 final questions to close this case for good: 1) I thought all solutions were given by span of \begin{pmatrix} 1 \\ 0 \\ 1 \\ -2 \end{pmatrix} , \begin{pmatrix} 0 \\ 1 \\ 0 \\ -1 \end{pmatrix} So where did this \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1...
  14. O

    Linear Algebra - Jordan form basis

    Ok, so I asked our instructor about the second question and yes, both methods are good. I prefer "my" method, but as you can see I still get stucked with it.. So how do I move on with this (A-3I)v_3 = λv_2+μv_4 ? Thanks again
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    Linear Algebra - Jordan form basis

    Hi, thanks for your kind replies. Ok, first I try what you suggested.. I take (A-3I)v_3 = λv_2+μv_4 I get: \begin{pmatrix} 1 & 1 & 1 & 1 \\ -1 & -1 & -1 & -1 \\ 6 & 1 & -4 & 1 \\ -6 & -1 & 4 & -1 \end{pmatrix}\begin{pmatrix} x \\ y \\ z \\ w \end{pmatrix}=\begin{pmatrix} λ \\ μ \\ λ \\...
  16. O

    Linear Algebra - Jordan form basis

    If it was a linear combination of other vectors then V1-4 would not be a basis.. Am I wrong? Plus, another student told me the method I tried was completly wrong and that the correct method is finding more vectors through Ker (A-λI)^j where j=2,3,... depends on how many more vectors I need...
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    Linear Algebra - Jordan form basis

    Hi all, I'm having trouble finding jordan basis for matrix A, e.g. the P matrix of: J=P^{-1}AP Given A = \begin{pmatrix} 4 & 1 & 1 & 1 \\ -1 & 2 & -1 & -1 \\ 6 & 1 & -1 & 1 \\ -6 & -1 & 4 & 2 \end{pmatrix} I found Jordan form to be: J = \begin{pmatrix} -2 & & & \\ & 3 & 1 & \\ & & 3 &...
  18. O

    Diagonalizability of a matrix containing smaller diagonalizable matrices

    Thanks for your reply. I still dont get it - I never said I found n eigenvectors. I said I found vectors for all eigen values of A and D. How can you tell A gives total of n1 and D gives total of n2 vectors?
  19. O

    Diagonalizability of a matrix containing smaller diagonalizable matrices

    Please don't mind my math english, I'm really not used to it yet.. Given R\in M_n(F) and two matrices A\in M_{n1}(F) and D\in M_{n2}(F) where n1+n2=n R = \begin{pmatrix} A & B \\ 0 & D \end{pmatrix} Given A,D both diagonalizable (over F), and don't share any identical eigenvalues - Prove...
  20. O

    Diagonalizability of a matrix containing smaller diagonalizable matrices

    Given R\in M_n(F) and two matrices A\in M_{n1}(F) and D\in M_{n2}(F) where n1+n2=n R = \begin{pmatrix} A & B \\ 0 & D \end{pmatrix} Given A,D both diagonalizable (over F), and don't share any identical eigenvalues - show R is diagonalizable. I'm building eigenvectors for R, based on the...
  21. O

    Contradiction of statement regarding monotonicity

    Will do. Thank you!
  22. O

    Contradiction of statement regarding monotonicity

    Hi all! We were given to proove or falsify the following statement: Given f(x)>0 \,\ ,\,x>0 \,\,\,\,,\lim_{x\to\infty}f(x)=0 Then f(x) is strictly decreasing at certain aεℝ for every x>a Now in their solution they contradicted the statement with: \newcommand{\twopartdef}[4] {...
  23. O

    Lim of An=n^2*exp(-sqrt(n))

    I've tried changing variables like you did and got m4/em, which does seem nicer.. But is using taylor expansion the only way to solve here? I'm pretty sure that's not what the course staff expected us to do..
  24. O

    Lim of An=n^2*exp(-sqrt(n))

    Hi all, my problem regards this limit: \lim_{n\to\infty}n^2e^{(-\sqrt{n})} Obviously equals 0, but I can't find how to show it. Tried the squeeze theorem (coudn't find any propriate upper bound) Ratio test won't seem to work.. I do realize the reason for that is that the set approaches 0...
  25. O

    Lim of An=(n+1)^(1/3) - n^(1/3)

    Yep, the trick is using a^3-b^3=(a-b)(a^2+ab+b^2) Thanks for your help anyway.
  26. O

    Lim of An=(n+1)^(1/3) - n^(1/3)

    This is the binomal theorem right? Is this the only way to solve this lim?
  27. O

    Lim of An=(n+1)^(1/3) - n^(1/3)

    Hi all! Been trying to look for some examples with no luck.. all I found is related to square roots, not cube roots.. Anyway I'm trying to solve: \lim_{n\to\infty}\sqrt[3]{n+1} - \sqrt[3]{n} The limit is obviously 0.. But how do I simplify this expression to show it? Or should I use the...
  28. O

    Recursive integral using integration by pars

    Hi tim, thanks for your kind reply :redface: Which "x" do you reffer to saying "and then use x as f or g" ? I've tried the trick you suggested using: g'=x^2+a^2 \quad\, \quad\ f=\frac{1}{(x^2+a^2)^{m+1}} but all I get is: \frac{arctan(\frac{x}{a})}{(x^2+a^2)^{m+1}} -...
  29. O

    Recursive integral using integration by pars

    First excuse my bad english on math subjects. I'm working on it. How can I integrate by parts: I_{m}=\int\frac{1}{(x^2+a^2)^m}\,dx I need to find a recursive form, But I can't find the right g' and f to get this done... I've tried g'=1 \quad\,\quad\ f=\frac{1}{(x^2+a^2)^m} As...
  30. O

    Diffrenetiating cos(yz^2)

    treat it like a=z^2.. It's a constant when differentiating with respect to y
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