Classical thermodynamics can be combined with relativity in order to accurately predict changes in mass and energy; before and after a thermodynamic process has taken place.

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### Thermodynamics, Engineering, and Relativity

Thermodynamics is a field of science dealing with heat and work transfer among the components of an isolated system. Engineers use thermodynamics to develop techniques and calculating tools for multiple applications such as fuel efficiency, refrigeration and air conditioning for internal combustion engines, turbomachines, rockets, nuclear reactors, etc.

Classical thermodynamics rely on four empirical laws that describe energy interactions and have been verified by experimental evidence. However, the extensive experimental and theoretical testing of thermodynamic laws has shown incompatibilities between the first and the second law. According to J.L.Tane, this was an indication that the existing theory needed to be extended and introduced the connection of conventional thermodynamics to relativity through the famous mass-energy equation of Einstein.

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### Classical Thermodynamics

In classical thermodynamics, the state of an isolated system (e.g. amount of gas enclosed in a vessel) can be described by a series of parameters/invariants: the pressure P, the volume V and the temperature T. The first thermodynamic law indicates that when the system evolves from an initial state (P

_{1}V_{1}T_{1}) to a final state (P_{2}V_{2}T_{2}), there is no change in the amount of internal energy U of the system:dU

_{1 }= dU_{2}This holds true regardless of the nature of the transition between the two states, reversible or irreversible (dU

_{irr }= dU_{rev}), and it is in fact in accordance with the conservation of energy principle. The second law of thermodynamics introduces a new parameter, the entropy S (measure of uncertainty or disorder) and states that the entropy can increase or decrease for reversible processes, while for irreversible processes it can only increase:dQ

_{rev}= TdS, dQ_{irr}< TdSand consequently dQ

_{irr}< dQ_{rev}where dQ is the amount of heat exchange between the gas and the rest of the isolated system, following our example.

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### Relativity and Thermodynamics

The classical thermodynamic theory lies on the idea that the mass within an isolated system is invariant with time, no matter if the process is reversible or irreversible. This admission doesn't take into account Einstein's famous mass/energy relation E = mc

^{2}, that revealed a new concept on how to explain inconsistencies between theoretical and experimental values of energy and mass before and after a process has taken place.J.-L.Tane proposed that the internal energy U of the system increases for irreversible processes:

dU

_{irr}> dU_{rev}More particularly, the increase in energy is accompanied by a decrease in mass:

dU

_{irr}= dUr_{ev}โ dE or dU_{irr}= dU_{rev}โ c^{2}dmand for the second law: dQ

_{irr}> dQ_{rev}The use of relativity has interpreted the increase in entropy, as an increase in energy, linked to a correlative decrease in mass. In other words, the concept of entropy has been substituted by the concept of increase in energy, making it unnecessary for the description of an isolated thermodynamic system.

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### Conclusion

The changes in mass introduced by this extended theory are generally too small and difficult to be experimentally detected. The conventional thermodynamic theory is thought to be sufficient in describing most of the systems that engineers are interested in. The extended theory could only be used in describing processes like nuclear reactions, so it is basically a theoretical tool. This new interpretation has yet to be recognized as valid, and hopefully further improved and extended by specialists in relativity.

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**References**- โThermodynamics and Relativity, A Condensed Explanation of their Close Connection", J.-L. Tane
- โThermodynamics, Relativity and Gravitation in Chemical Reactions. A Revised Interpretation of the Concepts of Entropy and Free Energy", J.-L. Tane, 2002.
- โThermodynamics and Relativity: A basic question about the behavior of living matter", J.-L. Tane, 2007
- โThermodynamics and Relativity: A short explanation of their close link", J.-L. Tane, 2007
- "Basic Chemical Thermodynamics", E. Brian Smith, Clarendon Press, Oxford, 1977