Corrections In Rest Energy

[Dubbelosix]

Planck considered, not long after Einstein proposed his famous rest energy equation and yet for some reason not specified in any literature ever took off, or any hint of why concerning its valid suggestions justifying the correction to the rest equivalence.

 

Planck suggested the correction of the form

 

[math] E=m_oc^2 + PV[/math]

 

To this I add, it may even be possible underthe total pressure

 

[math] E=m_oc^2 + int (P' - P) dV [/math]

 

It became apparently fortuitous that under the ideal gas laws or a photon gas meant To serve an alternative interpretation the relationship of the volume and mass to its latent energy. The photon gas law plays a direct role as

 

[math] E=m_oc^2 + PV = m_oc^2 + 3/2[sigma(4)/sigma(3)] Nk_BT[/math]

 

This further equivalates to

 

[math] E=m_oc^2 + 3/2[sigma(4)/sigma(3)]Nk_BT = m_oc^2 + 4/3 Int(U/T) dV = m_oc^2 + nRT[/math]

 

With (R ) being the gas constant.

Edited September 26, 2019 by Dubbelosix

[Dubbelosix]

From the last equation we can obtain a solution as related to the heat density

 

E = m_oc^2 + 4/3U + 1/2hv

 

With [v] being frequency. The last term was one of the first correction to his equation for his equation recognised also by the father of physics. It remains when the first two terms become negligible at near zero temperature.

 

The. Middle term can be illustrated in a whole new fashion by considering that energy is expressible as

 

E =Int[u/V dV] = U(dlog_V)

 

And from literature this is also aparrent in the form;

 

Log(T/T_o) = Log(V/V_o)

 

Interpretating the energy as we have been doing we shall finish for now with;

 

E = m_oc^2 + Int[u/V dV] + 1/2hv

 

= m_oc^2 + U(dlog_V)