โ Scribed by P.T Landsberg
No coin nor oath required. For personal study only.
It is noted that in a virtual displacement from an equilibrium state of a simple fluid subject to appropriate constraints (e.g., SS, = 6p, = 0), its energy and hence its inertial mass in the rest frame is increased: SM o > 0. In a general inertial frame 1, 6M > 0, the momentum is increased, and translational work 6Wt, is done on the system. It is shown here that the well-known condition 6H, > 0 in I,, gives rise to c2SM > SWt, in I (for a confined system). Analogous relations are set up for derived thermodynamic quantities A, (such as the free energy) by generalizing them to four-vectors Ap = A,U@/c, Ufi being the four-velocity, and by then considering the invariant scalar product (Up, aA*).
It is pointed out that the combination of thermodynamics and special relativity brings with it the system velocity as a new thermodynamic variable Ji)r all systenu, even in the initial rest frame,
๐ SIMILAR VOLUMES