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...
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?
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...
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?
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
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.
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...
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
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...
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
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...
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 &...
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?
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...
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...
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]
{...
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..
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...
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...
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}} -...
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...