Tuesday, September 30, 2014

\(\tau_o\) The New Guy On The Block

We would now formulate an expression for the repulsion between hot particles.  The simplest of which is to consider conservation of flux, as Gauss did

\(F_T=\cfrac{T_aT_b}{4\pi\tau_or^2}\)

where  \(F_T\)  is the repulsive thermal force between hot particles,  \(\tau\) is a measure of the resistance in establishing a thermal gradient between the two particles, and  \(r\)  the distance between the hot particles and,  \(T_a\)  and  \(T_b\)  are temperature on particle  \(a\)  and  \(b\).

Not bad for a first guess.

And so, for the post "Not This Way",

\(F_{ h }=Fsin(\theta )=\cfrac { q_{ p }q }{ 4\pi \varepsilon _{ o }r^{ 2 } } sin(\theta )\)

can instead be,

\(F_{ h }=Fsin(\theta )=\cfrac { T_{ p }T_e }{ 4\pi \tau _{ o }r^{ 2 } } sin(\theta )\)

and we are fine with diffraction on a straight flat edge.   \(T_p\) is the temperature on the photon and  \(T_e\)  is the temperature on the electron.

Hurra!  More importantly, the Universe now has a counter force to balance gravity.  Hot Banana Mochi safe.