Maxwell equation

  Maxwell thermodynamics relations(recall )

The Maxwell thermodynamics relations are a set of equations derived by James Clerk Maxwell in 1871. These equations describe the relationship between thermodynamic state variables, such as pressure, temperature, volume, and entropy. They are named after Maxwell because he was the first to describe them mathematically. The equations are used in thermodynamics to describe the behavior of systems in equilibrium. In particular, they are useful for predicting the properties of gases and liquids, which can then be used to model a wide range of phenomena.

The Maxwell thermodynamics relations are derived from the first and second laws of thermodynamics. The first law states that energy is conserved in a system. The second law states that entropy increases in a thermodynamic process. The equations derived by Maxwell describe the relationship between energy and entropy, and allow for the prediction of thermodynamic properties. The Maxwell thermodynamics relations have been used in various fields of study, including chemistry, physics, and engineering. They have been used to determine the properties of gases and liquids, and to model the behavior of systems in equilibrium. They are also used to predict the behavior of a system under various conditions, such as temperature or pressure. In addition, they are used in the design of heat engines, such as steam turbines, which are used to generate electricity.

Things that we have to know well deriving four type of Maxwell thermodynamics relations are

1. The first law of thermodynamics and its various formulations.

                du=Ts-pdv 2. The second law of thermodynamics and its various formulations.

                            ∆S ≥ 0 3. The definitions of specific heat capacity, heat capacity, and entropy. 4. The definitions of temperature, pressure, and volume and how they relate to each other. 5. The ideal gas law and how it relates to the other thermodynamic equations. 6. The definitions of work and energy, and how they relate to each other. 7. The definitions of enthalpy and Gibbs free energy and their related equations.

                            dH=Tds +vdp (for enthalpy)

                            
                    dG=vd_p-Sd_{T    (For gibbs free energy)}

8. The relationships between thermodynamic properties and their corresponding                             thermodynamic potentials. 9. The principles of statistical thermodynamics, including the Boltzmann distribution, partition         functions, and the concept of entropy. 10. The definitions of internal energy, Helmholtz free energy, and heat capacity. concepts                 such as partial derivatives, integrals, and the chain rule.

                         du=Ts-pdv(internal energy)

                        dF=-pv-sdT(Helmholtz free energy)

This are four Maxwell thermodynamics relations

                        

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