Recent content by raintrek

  1. R

    PhD Physics student on career planning

    Hi everyone - I'm hoping for a bit of impartial advice about career prospects for a couple of different options I'm considering. I graduated from a Masters degree in Physics back in 2009 and since then have been mostly traveling and working, albeit in an unrelated industry (medical...
  2. R

    Exploring the Significance of 1/4 in Kinetic Theory's Molecular Flux Formula

    The molecular flux (number of collisions per unit area per unit time) in Kinetic theory is given by F=\frac{1}{4} n \bar{c} where c bar is the average molecular speed and n is the density of molcules in the gas phase (molecules/m^3) I was wondering about the origin of the 1/4 term ...
  3. R

    Calculus: Find Gradient of θ Without Differentials of Arccos

    It's ok, I read the question wrong. Sorry about that folks
  4. R

    Calculus: Find Gradient of θ Without Differentials of Arccos

    Homework Statement I have the following expression: cos\theta = \frac{\vec{a}\cdot \vec{b}}{ab} (this is simply taken from a dot product rule for two vectors) However I need to find \nabla_{\vec{r}i} \theta Is there a way I can do it without involving differentials of arccos and...
  5. R

    Differentiating U_{ave} with respect to beta using summation notation

    Hmm, I've transcribed the problem straight from the question sheet. I too had that thought. I'm not sure I follow you with your methodology though. If I try to solve the equation using the standard quotient rule, it gives me zero - is there a reason for that?
  6. R

    Differentiating U_{ave} with respect to beta using summation notation

    Homework Statement Find \frac{dU_{ave}}{d\beta} where U_{ave}=\sum_{k}\left(\frac{U_{k}exp(-U_{k}\beta)}{exp(-U_{k}\beta)}\right) Homework Equations The Attempt at a Solution My answer is supposed to be -(U_{ave}^{2})+(U_{ave})^{2} However I keep getting zero. I can...
  7. R

    How Do You Calculate the Potential Energy Between Two Dipoles?

    LOL, ok probably talking to myself here. Still playing around with this, taken it further, although I'm pretty sure my final answer here is wrong... http://voy.trekcore.com/working.jpg
  8. R

    How Do You Calculate the Potential Energy Between Two Dipoles?

    OK, I've got a little bit further (this seems brutal!) I've been able to see that the separations of the charges mentioned above are: q1 & -q2: \sqrt{(d+rcos\theta)^{2}+(rsin\theta)^{2}} -q1 & q2: \sqrt{(-d+rcos\theta)^{2}+(rsin\theta)^{2}} Simplifying: q1 & -q2...
  9. R

    How Do You Calculate the Potential Energy Between Two Dipoles?

    Homework Statement Consider two dipoles with moments u1 and u2 arranged as in the following diagram. Each dipole is depicted as two charges of equal magnitude separated by a distance d. The centre-to-centre separation of the two dipoles is the distance r. The line joining the two dipole...
  10. R

    What Is the Entropy of a Two-State System at Zero and Infinite Temperatures?

    ^ Well the E/T term in the entropy would automatically go to infinity at 0K...
  11. R

    What Is the Entropy of a Two-State System at Zero and Infinite Temperatures?

    I'm having difficulty with this problem: Consider a two state system consisting of N distinguishable and indeppendent particles where each particle can occupy one of two states separated by an energy E. What is the entropy of the system at: (A) T=0 (B) T=infinity I'm assuming this...
  12. R

    How can I derive the formula using algebra for combining two equations?

    Dang, that will teach me to copy and paste! I'm sorry, Defennder, here's the correct expressions: \frac{V_{2}}{V}=\frac{p-p_{1}}{p_{2}-p_{1}}
  13. R

    How can I derive the formula using algebra for combining two equations?

    I'm trying to derive a formula but can't seem to work the algebra. I need to combine these two: V_{1}p_{1} + V_{2}p_{2} = N V_{1} + V_{2} = V to get this: \frac{V_{1}}{V} = \frac{p-p_{1}}{p_{2}-p_{1}} where p = N/V If anyone could show me the steps that would be a huge help...
  14. R

    Molecular Simulation Research Ideas Needed

    Hey all, I'm looking for some suggestions on topics concerning Molecular Simulation which I can research. I've been tasked with giving a talk and writing a report on one specific topic of this field but I'm unsure what to specialise in. Any and all advise and suggestions would be appreciated!
  15. R

    How to Show Derivatives of 1/R for a 1D Charge Distribution?

    Homework Statement (Lead into question: "Assume that charges +q, -3q, 2q lie at positions -2a, 0, +2a along the x-axis respectively.") I've calculated dipole/quadrupole moments about the origin as well as the exact potential at x=+10a, however I'm confused by this next part to the...
Back
Top