Recent content by A-fil

Homework Statement Give an physical explanation to why the specific heat capacity goes to zero as temperature goes to zero. Homework Equations The Attempt at a Solution I was simply thinking that around absolute zero the average kinetic energy of the particles should be zero...

Ohh, thanks! That would give me what I'm looking for (see below). However, I still don't fully understand why. Is it because we integrate over all of the room V and for all speeds v, so whatever inital energy particle number i had doesn't really matter, meaning that we can say that all particles...

Hehe, the integral thing was a classical case of me being tired. Thanks for replying! So, I get to this: Z = \int_{V}d^{3} r_{1} ... \int_{-\infty}^{\infty}d^{3}v_{N} e^{-\beta E} = \int_{V}d^{3} r_{1} ... \int_{-\infty}^{\infty}{d^{3}v_{N} e^{\sum_{i=1}^{N}{-\beta...

I've got a few problems that I got stuck on. I'll add more problems in this thread as time passes. Homework Statement 3.5 Show that Equation (23) holds for any classical system that has a total energy of the form E = \sum_{i=1}^{N}{\bf{ϵ}(\bf{v}_{i},\bf{r}_i)} where ϵ(v_i,r_i) is any function...

If you don't know how to calculate determinants then that's not necessary in this problem. You can look at the equations one at a time, starting with the one that only contains x. Now, depending on λ, x may be forced to have certain values. If x,y and z isn't forced to have certain values...

Thanks both of you for your help! I think I got it, but just to make sure (and for others who might have gotten stuck on something similar) I'll write it down. f(y)=P(Y \in (y,y+dy)) = \sum_{i=1}^{\infty} P(Y \in (y,y+dy)|N=i)P(N=i) We know that P(N=k)=(1-p)^{k-1}p To calculate the...

Homework Statement Let X1, X2, … be independent exponentially distributed stochastic variables with parameter λ. For the sum Y = X1 + X2 + … + XN, where N is a geometrically distributed stochastic variable with parameter p, show that Y is exponentially distributed with parameter pλ...