update:
I spoke to a professor from the Thermodynamics department, and apparently, there's an error on the original exam sheet. During this particular examination, they made it known to the students then and there that where it said:
"The wall is free to move back and forth and is not...
That would be nice of you. I think I have the book here somewhere (the 6th edition), so I'll try and look for it in the Entropy chapter. If I can't find it, I'll let you know. :biggrin:
I see, that's interesting. Did you actually happen to see how the components of the compressor moved, that is, if it's safe to assume that it moved in a quasistatic manner? Because if it did, then I may have my answer. :biggrin:
Are you sure the process can be considered polytropic? I mean, the expansion of one gas/compression of the other seems like an internal irreversibility to me, so during that process, the pressure isn't a well-defined property (you got turbulence and in general a fairly complicated gas dynamics...
Hm, and also, m*Cv*delta T happens to be the change of internal energy, so if I use that formula, it'd be like saying that neither gas does work, nor has work done on it. Is that true in this case?
Hello, LawrenceC! Thanks for replying. :smile:
Nothing crosses the boundary if we take all of the system, and the total internal energy of the system remains constant; internal energy of an ideal gas is solely a function of temperature. As you can see, I've already used all this to obtain the...
Hey, thanks for answering. :smile:
Well, your particular question is addressed in section 4 of the article. They state:
The first thing they do to answer the question is to consider the high temperature reservoir:
They then introduce a modified heat engine, where the high temperature...
The I in my explanation was the I of an arbitrary branch in which a shortcircuit is produced, I didn't use the same circuit as the one given. That's why I said V = IR, and not V = (I-i)R.
The I of my example would be extrapolated to whatever it need be, per particular circuit.
So, I've read in books and on Wikipedia (see for instance http://en.wikipedia.org/wiki/Carnot%27s_theorem_%28thermodynamics%29#Applicability_to_fuel_cells_and_batteries) that the Carnot efficiency cannot be applied to a fuel cell because it is not a heat engine that produces work, operating...
AB seems to be a shortcircuit. That is a potential difference of 0, so if you end up getting that, it's nothing to worry about. If you got something other than 0, that's when you should be worried. :wink:
Basically, you can think of a shortcircuit as taking a branch with a single resistor R...
Homework Statement
A horizontal container with adiabatic walls has a vertical wall inside it which divides the container in two. The wall is free to move back and forth and is not adiabatic. Initially, 1 kg of air is in the compartment to the left of the wall, at 5 bar and 350 K, and to the...
I am well aware that there is no such thing as a body with infinite rigidity. However, within the framework of Classical Mechanics, where perfectly rigid bodies are allowed, this loss of energy is what surprised me. :biggrin:
AlephZero, D H, thanks a lot for the interesting discussion and interesting points you have raised.
However, one thing still bothers me. AlephZero, you have said that the kinetic energy changes in this problem because it is an inelastic collision. Usually, in an inelastic collision, changes...
Thank you for taking the time to read my message, AlephZero. :smile:
Another thing that's interesting about the book's solution, or equivalently, the one you presented with conservation of angular momentum, is that there is a difference in initial mechanical energy and final mechanical...
Hey, all!
Browsing around the library for some mechanics books, I happened to come across Manuel Prieto Alberca's Curso de Mecánica Racional. Dinámica. In this book, I managed to find an interesting problem that is also solved, but having talked to other people, I have started to suspect that...
Hey, all.
I'm tutoring a freshman, and we've come to this particular problem, and I think there's missing data. He does have access to the vapor tables, but as you can see, he's not given total mass, volume, nor any specific heat... here goes:
"An adiabatic calorimeter contains a water-ice...
Hey, micromass.
Thanks a lot for the info, I sort of had a sneaky suspicion this was related to de Rham cohomology. I'll give that book a read, thanks a lot!
Hey, all.
Anyway, I've been looking at books and sources online, and the only counterexample to the wrongly stated theorem
\nabla \times \mathbf{F} = 0 \Leftrightarrow \text{conservative vector field}
seems to be \mathbf{F} = \left(\frac{-y}{x^2+y^2}, \frac{x}{x^2+y^2} \right),
or other...
Be careful, you are not trying to optimize the constraint itself, but rather another function subject to the constraint.
You have two ways to solve it.
You are trying to find the minimum vale of S(x, y) = x+y, subject to the constraint y(x+2) = 9. So one way would be to solve for y in the...
Thanks for all the input, micromass. It may be possible to locate the original MATYC issue in question and see if there is indeed a typo and the integrand is messed up and/or it's actually a definite integral.
While it's true that most integrals that one can think of have no elementary antiderivative, WolframAlpha claims that it can't find a result in terms of standard mathematical functions that it knows - and Wolfram Alpha knows many non-elementary functions like the Gaussian (erf and erfc) and sine...
Hey, all.
Anyway, browsing the Internet a bit I found this integral:
\int \sqrt{1 + \frac{\ln x}{x}}dx
as a proposed problem in a compilation of maths problems, as an integral from the MATYC journal. I gave it to Mathematica and WolframAlpha and they weren't able to solve it...
There's a problem with personalized compilations - different people require, in general, different formulas depending on their background, what they do research in, what they work with, etc... but the most usual formulas are found in popular handbooks, such as...
For some Frobenius series expansions, in addition to the indicial equation, additional transition equations may appear that allow you to determine the c_i, where i is some number in \mathbb{N}. In this example, you should have an additional transition equation to determine c_1, and the final...