Not meaning to bash Smith and VN at all. In fact, it's one of the only thermo books I've read that discusses this topic in any degree. I just wished they would've explained more since they are my only source on the subject!
Framing the question is definitely part of the problem, because since V, U, & H for an IG can all be evaluated at the total P, then Gibbs theorem seems to be the exception instead of the rule, with the exception being S (and anything related to S). I don't know what kind of answer I was looking...
In the chemical engineering text of Smith, VanNess, and Abbott, there is a section on partial molar volume. It states that Gibbs theorem applies to any partial molar property with the exception of volume. Why is volume different? In other words, when evaluating the partial molar volume of a...
Awesome find. This is what I've been looking for. I'm glad it somewhat validates mine/your thoughts about ball deformation causing more energy loss. However, the thing that I still cannot wrap my mind around is using conservation of momentum to view this situation. Momentum is always conserved...
Obviously, it's not tennis without the player. But your answers were far off-topic, so I wanted to get you to think about it in a physics sort of way. Simplifying the situation to just a fixed racquet and a dropped ball is still helpful. This is what much of physics is about, simplifying nature...
I don't like the link you posted b/c it's just rehashing the same old information I've always heard in the tennis community without explanation.
However, the 2nd point you bring up about ball deformation is actually something that I have wondered about. Could it be that since tighter strings...
This isn't really answering my question of whether or not there is any truth to the "loose strings give power, tight strings give control" claim. I'm looking for a scientific explanation of why looser strings would generate more power in a shot. If it helps, take the person swinging the racquet...
You're reply only confuses me. Assuming that the loose fishing net is elastic, then in my conceptual model, it wouldn't change how fast the ball leaves the racquet. No energy is lost, therefore, it all ends up back in the ball as kinetic energy. Right? Also not sure what you're talking about...
I have a decent background in physics, but something that has always confused me is how to think about how the tension of the string in a tennis racquet affects how the ball leaves the strings. For example, the traditional lore in tennis is that tauter strings will give more control, whereas...
Let's talk about specifics. Say there is a BB sphere in a vacuum, and then there is a medium with n>1 after light passes through the vacuum. So you're saying that the reason the emissive radiation increases is because the radiation emits from the BB, travels through the vacuum, then some of it...
Not sure if that makes sense to me. First of all, can you describe the geometry a little better (spherical, a wall, etc)? Second of all, you mentioned "reflection", however, Planck's law doesn't say anything about reflection. It is only describing the power intensity radiating from a BB. If...
This question is regarding the dependence of Planck's law for black-body (BB) radiation intensity (or integrating over a hemisphere, the emissive power, E = pi * I).
Physically speaking, why is it that a BB emitting in a medium with n>1 (n being index of refraction) emits a higher power/area...
Yes, the answer is that the water in the microwave gets superheated: heated to a temperature beyond its boiling point, but it does not boil. Then, when you add your tea ball to the water, it provides the "activation energy" and starts the boiling process via nucleation sites. Also, FYI, the...
I tried to be as clear as possible (stating that I understood state variables, hence that was not my source of confusion), and apparently it was communicated well enough for the poster below to perceive the correct question and answer it.
This is what I needed, thanks.
On page 200 in the 7th edition of Intro to ChemE Thermodynamics by Smith, Van Ness, and Abbott, there is an equation that has always bugged me since reading it (or rather the interpretation of it, not the derivation). It is equation 6.1 and states:
d(nU) = T d(nS) - P d(nV)
with n = moles in the...
If I'm interpreting your situation correctly and based on what has been calculated above as the average energy you could theoretically transfer if the entire tank was brought to 25 C and given that you said your shop is very large, this seems like a futile endeavor to recover that energy to heat...
You're definitely right that I'm rusty on my ΔG interpretation (its been a few years since I did these calcs in a good thermo class), so I'll take some time and do some thinking, then hopefully I won't forget to come back for any lingering questions. Appreciate the help.
But you can still calculate a G value for it. Even though the EQ state of water is ice at -10C, this doesn't mean that there is not a G value for liquid water at -10C. For example, as I'm sure you're aware, if you start with liquid water above 0C and carefully cool below the freezing point, you...
You may be right that this is what I'm looking for, because almost by definition, for a chemical reaction, we are talking about microscopic particles, but for a block of ice, it's large.
(EDIT: but since we know everything is made of atoms, is there really such a thing as static EQ? I think...
Chet
Yes, this is getting to addressing my original question. OK, just to be clear, let me go through this scenario with a chemical reaction.
N2(g) + 3 H2(g) 2 NH3(g)
[PLAIN]http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch21/graphics/delta.gifGo [Broken] = -32.96 kJ
Alright, lets assume...
I see your point but I'm not sure that dG/dξ is anymore correct than ΔG, since, for any process that has reached equilibrium, the total G's (regardless if the process was discrete or continuous) from beginning to end or from reactant to product must be equal, otherwise the system could lower its...
Are you suggesting that at a given T & P that the criteria for spontaneity is something more than ΔG < 0? My knowledge of thermodynamics relies on the fact that at a const T, P the only criteria for a process being spontaneous thermodynamically is ΔG < 0.
You don't need to convince me of this. I'm sure this plays a role, but it's not addressing the question I posed. I only posed a question concerning the magnitude and sign of ΔG. Sure, the entropy of mixing will have a role on the value of ΔG, but that is outside the scope of my question. My...
I'm familiar with this, but I was assuming everyone understood me to mean -4 C and atm pressure. This entire conversation becomes trivial if we allow pressure to vary to let water thermodynamically favor liquid at -4 C and some P.
As of now, I don't think it has anything to deal with single vs multicomponent systems. I have talked to number of people about this issue recently, and what we seem to have concluded is just that the ΔG for the ice melting (at -4 C) is so largely positive that you will never macroscopically...
If we have solid water (ice) at -5 C and atm P, then according to thermodynamics, the process that takes that ice (at -5 C & atm P) from solid to liquid is non-spontaneous, which means its ΔG > 0. Hence, it is impossible for someone to observe ice melt to liquid at -5 C, and assuming we started...
Homework Statement
"Show that the Slater Determinant states are a complete basis" is the entire statement.
Homework Equations
The Attempt at a Solution
I guess I'm trying to prove that the rank of the states is equal to the basis? I'm not sure where to start on this one.
Thanks for your answer.
I guess I was just confused because I'm still in the part of the book that is talking about the free electron gas, hence ε ∝ k^2 and cannot be negative. But you're saying that ε can take different forms than the expression I used, just depending on the potential the...