Homework Statement
There are 2 versions of the problem that I've heard:
A bucket on wheels is moving at a constant velocity on a frictionless surface. It's raining out so the bucket is gaining mass. Will it slow down, speed up, or remain at that velocity as it gains mass?
A cart loaded...
Homework Statement
I haven't been assigned these questions, but I'm trying to trudge through them to better understand symmetry. This is for my inorganic class.
It's just a series of short questions like:
C3 – S56 = ?
S4 + i = ?
C3 + i = ?
Stuff like this. And just looking at the...
Actually, the two methods don't give me the same answer. If I use wC = -(wA + wB), I get wC = 458.027 kJ, and q = ΔU - w = -227.683 kJ.
If I take ΔU of the entire system to be qC, then I get -1143.737 kJ. I'm not sure, but why would w = 0 for the entire system?
EDIT: I just re-calculated it...
Ah, sorry, for the first one I meant q = ΔU - wC = ΔU - [- (wA + wB)].
For the second, his rationale is that you can take the process stepwise, and calculate the q for first the isothermal, reversible expansion (q = nRT ln (Vf/Vi), where T = 300 K), and then calculate q for the isochoric...
Because of the autoprotolysis of water? So we'd use Kw = 1 x 10–14 to get OH- in terms of H3O+, correct? But this doesn't change the pH by an appreciable amount does it?
One thing I was struggling with was how to factor the 0.1 M contribution of the OH- into the charge balance. Does the right...
So, it wouldn't be correct to use q = nRT ln (Vf/Vi) + n \int_{700}^{300} \bar{C_{v}}dT? That's what my friend thinks is correct; essentially it's the same way we found ΔS, but we aren't dividing by T, because ΔS = q/T.
Wouldn't there be expansion work against volume in chamber B and A that...
Yes, you're correct of course. I noticed that later on but forgot to edit it in. Also, I believe my mass balance neglected [H3PO4]. But the pH of 7.3 was after correcting for these. Oddly enough, I got around 10 after adding NaOH, however my friend got 12; not particularly sure why.
Also...
Homework Statement
In a 3-chambered system, separated by 2 pistons, all of the walls are adiabatic, except for the wall on the outside of chamber C (the wall marked }).
[A | B | C}
The pistons are frictionless, the gas fills all 3 chambers and is ideal, and \bar{} = R. Total volume = 12...
Yeah, I know there's going to be very little [PO43-], but our prof wants us to calculate it as if there will be. And yeah, he does want it done the long way. It's a terrible equation, but wolfram alpha helped me get the final answer, which, if I did everything right, should be about 7.351.
Homework Statement
8.9985 g of Na2HPO4 and 4.0211 g of NaH2PO4 * 7 H2O are added to 1 L of 0.20 M KCl in water. KCl does not participate in any way but to maintain ionic strength, at 0.20 M.
H3PO4 (aq) + H2O → H2PO4- (aq) + H3O+, Ka1 = 7.11 x 10-3
Ka2 = 6.32 x 10-8
Ka3 = 7.1 x 10-13
(a)...
That was the equation that I ended up using when I revised my answer. In the end, I got that at 100 K, ΔG = –68.6 kJ. Our professor also had us approximate the value using the Gibbs-Helmholtz equation, which gave me –72.6 kJ. It makes sense for the two values to be off, because I know the...
Homework Statement
"Estimate the standard reaction Gibbs energy of the following reaction:
N2 + 3 H2 ‒‒> 2 NH3
at 100K and at 1000K."
Homework Equations
ΔS(T2) = S°(T1) + ∫ n Cp dT/T
ΔG = ΔH ‒ TΔS
Given data: http://imgur.com/MBakUEB (may need to right-click and select...
So I've been slowly plodding through this problem, and so far this is what I've done:
Took partial of ##x##, factored out the ##e## term and canceled it, because it can never equal ##0##.
So ##x^2+4y^2-1 = 0##
Same with the partial of ##y##: ##x^2+4y^2 = 4##
Now, these are ellipses...
Homework Statement
Consider the function f(x,y) = (x2 + 4y2)e(1-x2-y2)
Find all critical points, and identify them as maxima, minima, or saddle points.
The Attempt at a Solution
I took the partial of x and the partial of y, and set them equal to 0. This is what I got:
fx(x,y) =...
Homework Statement
Predict the major organic product of the following reactions:
The Attempt at a Solution
For 1, I got:
And for 2, I got:
If anyone can help confirm, I'd be much obliged! Our professor is crazy and gives these types of problems for practice...
Hmm. I'm guessing since they're orthogonal, ##\int {\vec B \cdot d\vec s} = 0##, right? Okay. That makes perfect sense, thank you!
Actually, on the subject, I was wondering about something that I saw on a website somewhere. Apparently, the graph of B vs radius of a solid, cylindrical...
I just have a quick question about how to use Ampere's Law. It says that ∫B ds = u0(i_enc), which I suppose is easy enough to understand. But I'm having trouble reconciling it with the notion of, say, the magnetic field at the center of a loop of wire.
The magnetic field at the center of a...
Homework Statement
Find the current through the 100 Ohm resistor:
http://imgur.com/sohdpyE
The Attempt at a Solution
So I was able to simplify the 100 and 500 resistors, as well as the 20, 20 and 10 series resistors, but I can't seem to discern at all whether any of the remaining ones...
Homework Statement
Let f(x,y,z)=u(t), where t=xyz. Show that f_{xyz} = F(t) and find F(t).
The Attempt at a Solution
I'm a little confused about the presentation of the variables in this problem. What does F(t) refer to? This isn't a chain rule question, because it's presented before chain...
I realized that a few minutes after I posted it, my bad!
So we've got f_{x_k}=kx_x.
The function f described by this set of partial derivatives should be in the form f(x_1, x_2, ... , x_n), right? So I run into a bit of a snag when we integrate that partial.
If f_{x_1} = x_1, then...
Homework Statement
f'_x = kx_k, k = 1, 2, ..., n
The Attempt at a Solution
The partial should be f(sub)x(sub)k, as in, the partial derivative of f with respect to x_k. I wasn't sure how to represent that using TeX.
I'm honestly at a complete loss here, because I'm not entirely sure what...
That was brilliant! Splendid hint, it was all I needed to get the answer, thank you!
Just to confirm, dotting ##\vec v_1## into both sides left me with c1|##\vec v_1##|2 = 0, which of course implies that c1 = 0. I repeated by dotting ##\vec v_2## into the original, and by the same process...
Homework Statement
1. Suppose that u + v + w = 0. Show that u x v = v x w = w x u. What is the geometric interpretation of this result? (Note: The interpretation should explain both the length and the direction).
2. Let v1, v2, and v be three mutually orthogonal vectors in space. Use the...
You were right, there was a mistake in my signs.
c2 = (w2 – w1)/2
c1 = (w2 + w1)/2
That should be right.
And in fact, when I plug in these values for c1 and c2 in the c1<1, 1> + c2<-1, 1> expression, after simplification I am left with <w1, w2>.
So, the expressions for c1 and c2 we...
Okay, I think I might have it.
So say w = v1 + v2, in which case w = <0, 2>. Hence, w1 = 0 and w2 = 2.
So:
c1 – c2 = 0, so c1 = c2
and c1 + c2 = 2
But c1 = c2, so
c1 + c1 = 2
2c1 = 2
c1 = 1
Hence c2 = 1.
But the problem I have is that we calculated c1 and c2 to be 1, but...
I'm sorry, I'm not entirely sure I understand what you're saying here. When you say we're given ##w_1## and ##w_2##, do you mean what we have just found, i.e. ##w_1## = <##c_1## – ##c_2##>? Or do you mean ##w_1## was something that was given to us earlier in the problem?
And I'm not sure I...
Hmm. I suppose that makes sense, I might have overlooked that fact. So then,
<w1, w2> = <c1 – c2, c1 + c2>
w1 = c1 – c2
w2 = c1 + c2
So the horizontal component of our vector w was shown to be c1 – c2, and the vertical component was shown to be c1 + c2. Alright, that's cool. Is that then the...
Homework Statement
Let v1 = <1, 1> and v2 = <-1, 1>. Show that for any vector w in the plane one can find constants c1 and c2 so that w = c1v1 + c2v2. (Hint: Express w in component form and obtain two linear equations for the unknowns c1 and c2.
Homework Equations
The Attempt at a...