Recent content by Ionophore

Hi all, I’m trying to distribute M balls into N boxes. Each box has two compartments (thus 2N compartments total), each of which can hold one ball. There are more compartments total than balls. What I would like to do is calculate the number of boxes, on average: 1) With no balls (2...

So: \int_{\vec{r}} \frac{\delta(\abs{|\vec{r}|-L})}{2\pi L} \vec{r} d\vec{r} = \int_{r_{x}} \int_{r_{y}} \frac{\delta(\abs{|\vec{r}|-L})}{2\pi L} r_{x}r_{y}dr_{x}dr_{y} Where r_{x} and r_{y} are the components of \vec{r} , and the integrations extend from -infinity -> infinity. I...

Whoops, I'm sorry, I did mean magnitude: \int_{\vec{r}} \frac{\delta(\abs{|\vec{r}|-L})}{2\pi L} \vec{r} d\vec{r} So, then, I am to understand that the above is really a double integral? What is meant by r_i, dr_1 and dr_2?

Hi, This is probably a really simple question, but I think that I am getting lost in notation. I want to integrate the following over all values of the (2-dimensional) vector \overline{r}: \int_{\overline{r}} \frac{\delta(\abs{\overline{r}-L})}{2\pi L} \overline{r} d\overline{r} Basically...

Yes, the concentrations of specific proteins are heavily regulated in response to environmental conditions. There are a lot of ways this is accomplished, including reduced transcription of the gene in question, degredation of mRNA transcripts, and degredation of the protein post-translation.

Can someone give me a hint on how to evaluate the following limit? \stackrel{lim}{T\rightarrow\infty} (Texp(c/T) - T) I tried multiplying the numerator and denominator by the conjugate (because that sometimes helps) and got: (T^2exp(2c/T) - T^2) / (Texp(c/T) + T) But I'm not sure what I...

I think that that example is better. Another one that I can think of is suppose your system is a ball on a string hanging from a ceiling. If the ball expands as you raise the temperature its center of mass is lowered, and, with appropriate dimensions and expansion coefficients, I think you...

Is it valid to use dU=C_vdT in such a problem? The volume is changing, so how can we use C_v? But perhaps we are near the answer. For U to be independent of temperature we would require C_v =0. This would require T(dS/dT)_v = 0. So it appears that U is independent of T when T=0, but when...

"The fact is, however, that in thermodynamics temperature of a system IS DEFINED as the average KE of the molecules of the system." I don't want to argue too much about this, although I am not sure I'm ready to accept that idea outright. One concern I have is that in isolated spin systems it...

Yes, the internal energy is relative. According to Callen (page 12): "Only differences in energy, rather than absolute values of the energy, have physical significance, either at the atomic level or in macroscopic systems. It is conventional therefore to adopt some particular state of a...

It is correct to include the potential energy of the icicle as part of the system's internal energy. T being a measure of the average KE of the molecules in the system is a statistical mechanical idea that is absent from classical thermodynamics - to the best of my understanding.

... On second thought, maybe I don't like it. As the icicle falls, its gravitational potential energy is converted to kinetic energy, so it doesn't lose anything. When it hits the ground it will either dump that kinetic energy as work (perhaps it lands on a paddle wheel) or heat. Regardless...

Very nice example! I like it! And thanks for all the help everyone. -Ben

Right, in this case u depends on both v and T. But in general, must u depend on T? This is something that I have wondered for a very long time. It seems intuitively obvious that u should always increase with T, but I'm not sure I can nail down any bit of the theory thus far developed in...

"If it is a free expansion (no work done, no heat flow), wouldn't the first law of thermodynamics require U, hence T, to be constant? " But most generally, must U depend on T?