# Search results

1. ### 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. ### 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?
3. ### 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.
4. ### 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...
5. ### 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 &...
6. ### 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...
7. ### 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...
8. ### 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] {...
9. ### 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...
10. ### 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...
11. ### 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...