Thursday, November 9, 2017

Going Back To Durian Constantly

If we indulge in the what ifs and maybe's especially from the post "A Constant Serial Killer" dated 12 May 2016, where the Durian Constant,

\(A_{\small{D}}=\cfrac{4}{3}\pi(2c)^3\)

and

\(R=2*\cfrac{4}{3}\pi=8.377580\)

From the Kinetic Theory of ideal gas,

\(v^2_{rms}=\cfrac{3RT}{M_m}\)

\(v^2_{rms}=\cfrac{3*2*\cfrac{4}{3}\pi T}{m_a\cfrac{4}{3}\pi(2c)^3}\)

where \(m_a\) is the mass of one gas particle.  We have,

\(\cfrac{1}{2}m_av^2_{rms}=\cfrac{3T}{(2c)^3}\)

temperature \(T\) is just the average kinetic energy of one free gas particle scaled by a factor, \(\cfrac{(2c)^3}{3}\)

\(T=\cfrac{(2c)^3}{3}*\cfrac{1}{2}m_av^2_{rms}\)

The factor \(\cfrac{1}{3}\) accounts for any one direction of travel of the particle in a \(3D\) volume and \((2c)^3\) is the volume containing all the particles numbered in one Durian Constant, within which they are all entangled.

This does not validate \(T_{boom}\), but shows in general what \(T\) here measures as oppose to the number of  \(T^{+}\) or \(T^{-}\) particles.  \(T\) indicates the total kinetic energy of all the particles within a \((2c)^3\) volume, along one particular direction.

If \(m_a\) is in mass density then, the term

\((2c)^3\)*m_a

is the total mass within the volume.  With the factor \(\cfrac{1}{3}\) we are concern only with one of the three orthogonal directions in space.

Have a nice day.