Abstract
The first Principle defines, for every system, a property named energy which is a conserved quantity and this means that its variations in a process, can be due only to the interaction with the external world. The latter interactions are divided into two groups. On one side, we consider all the interactions which are described within some theoretical contexts developed up to now. We say that these are the interactions controlled by the observer. In the second group, we place all those interactions which are unknown to the observer or which are treated as such. The cumulative effect of these unknown interactions gives rise to one term which is currently called quantity of heat. After having defined the meaning of adiabatic transformation, experimental evidence shows that in the latter case the amount of work delivered by the interactions controlled by the observer in a change of state depends only on the initial and final states and does not depend on the transformation used. This defines energy and, as a consequence, the contribution of the unknown interactions in a generic transformation, that is the amount of heat, is defined by the difference between the variation of energy and the amount of work carried out in that transformation. All this needs to be formulated for closed (with respect to mass) systems.
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The particular form of the Lorentz factor derives from the postulate on the invariance of the speed of light. This postulate affirms that a light signal is seen to propagate (in vacuum) with the same speed when observed from any inertial frame of reference. This postulate, together with the adoption of the Principle of Relativity, leads to a well-defined form of the laws of coordinate transformations between two different frames of reference called Lorentz transformations. Two popular consequences of these transformations are known as the length contraction and the time dilatation. Both these effects scale with the Lorentz factor.
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Saggion, A., Faraldo, R., Pierno, M. (2019). The First Principle of Thermodynamics. In: Thermodynamics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26976-0_2
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DOI: https://doi.org/10.1007/978-3-030-26976-0_2
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