Help with Maxwell: Understanding 6 Dimensions of Space

[hikaru]

I read a school subject book by test measures and have intended in doubt.

What I can understand is not readily found in search of other references either. Please help it.

When I considered gravity, dynamic energy thought about a (x,y,z) coordinate and a speed ingredient of a molecule at the same time to demand it with kinetic energy + potential energy and was able to understand that I thought as 6 dimensions of space.

f(x,y,z,vx,xy,xz)dxdydzdvxdvydvz = C exp(- ε /kT)dxdydzdvxdvydvz

　* ε = m/2(vx^2 + vy^2 + vz^2) + φ(x,y,z)

Though I understand it, how will be that C is the fixed number if I try to really demand C?
I tried to demand it from oneself, but it is it and has it at all and is not confident of a different value whenever I demand it. It is C = (mg/2kTS)*(m/2kT π )^ for the time being(3/2) 　I became the value that was とsufferings from unjustness tea to say, ； It was it in this way when I thought as the case that I classified into a container expensive endlessly of cross-section area S. . .

In addition, how should the mean of dynamic energy demand it in this case? In addition, as for the found value, it seems to be it in a value different from mean (3kT/2) of dynamic energy of the ideal air which does not consider gravity hereby. Why seems to be ・ ・ ・?

 

[Jezuz]

I read a previous post from you. Your english is a little confusing so it is a little hard to understand what you mean. I think what you should do to calculate C is to require the distribution function to be normalized. So that
\int_{-\infty}^\infty f(x,y,z,v_x,v_y,v_z) dx dy dz dv_x dv_y dv_z = 1
You can can calculate this by the use of Guassian integrals and then you should obtain the value of C.

 

[hikaru]

Thanks a lot.