Abstract
Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction term. Finally, we apply our coupled evolution equations to study the thermodynamics of an isolated system consisting of identical point particles interacting through a harmonic potential.
Highlights
The history and development of modern thermodynamics started during the industrialisation period and was closely related to the need to improve the efficiency of steam engines
In that system of differential equations, the coupling between the resulting Lagrange equations and the thermal equation is due to the viscous friction terms depending on the state variable
If the state functions U and λij are independent of S, or equivalently, if the time evolution happens at fixed temperature by contact with a thermal bath, the mechanical Lagrange equations decouple from the thermal equation
Summary
The history and development of modern thermodynamics started during the industrialisation period and was closely related to the need to improve the efficiency of steam engines. The second law of thermodynamics requires the existence of a state function entropy for every system. Applying the first and second law, we obtain a system of coupled differential equations describing the thermodynamic evolution of the system.
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