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of calorimetry, and whether the original operations can be sufficiently broadened is to my mind very questionable. At least I have never seen any adequate discussion of the possibility."
From I?. W. Bridgman The Nature of Thermodynamics (Harvard 1941; Harper Torchbooks 1961, p. 29) 1. 1NTRODUCTION
Most authors have approached the problem of identifying the Lorentz transformation of heat dQ given to a system in an incremental process, by first considering the transformation of mechanical work dW in the same process. Since different answers have been obtained to this fundamental question, (Z-5), we consider it here in a generalised way which enables one to see the answers recently given in a single context.
This generalised calculation of the work done on a moving system faces two main difficulties, both of which are solved in this paper. The first difficulty resides in the multiplicity of inertial frames, each with its own proper time, which enter into the calculation. The process of compression or expansion may start simultaneously for all surface elements of the system if the inertial frame used is the initial rest frame I,, of the system. But at the end of the process the system will in general be at rest in a different inertial frame. However, the calculation of dW is in any case required for a general inertial frame I and in such a frame the surface elements start to accelerate relative to the centre of mass at different times. The centre-of-mass frame has initially velocity w, in I, and when the last element has ceased to accelerate relative to the centre of mass the rest frame may have a different velocity, w + du, say, in I(& < w). The analysis required to deal with these questions is rather delicate, and will be found in the Appendix.
The second difficulty is that the calculation of dW must hold for two different definitions of force which have been used. It is possible to handle this situation by operating throughout with a definition of force which is sufficiently general to accommodate both points of view. This is achieved by using a parameter p with value 0 or 1 for the two definitions (see Section 2). It is found, as one would expect, that the transformation of both dQ and dW depends on this parameter (see Section 4).
An adequately general discussion must include a further complicating feature. Special relativity deals with systems for which the energy-momentum four-vector is PI" = (cP, E) and systems for which it is Pzw = (cP, E + pV). The former systems are the unconfined systems of particles, and thermodynamics cannot readily be applied to these, since they are not equilibrium systems. For a normal confined equilibrium system to which thermodynamics can be applied, P,@ is the relevant quantity. However, the simpler quantity Plu becomes again appropriate
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