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The generalized force, X, corresponding to the external parameter x is defined such that is the work performed by the system if x is increased by an amount dx. E.g., if x is the volume, then X is the pressure. The generalized force for a system known to be in energy eigenstate is given by:
The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions.A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient).
The second law refers to a system of matter and radiation, initially with inhomogeneities in temperature, pressure, chemical potential, and other intensive properties, that are due to internal 'constraints', or impermeable rigid walls, within it, or to externally imposed forces.
where is the thermal conductivity of the material, = (,) is the temperature, and = (,) is a vector field that represents the magnitude and direction of the heat flow at the point of space and time . If the medium is a thin rod of uniform section and material, the position x is a single coordinate and the heat flow q = q ( t , x ) {\displaystyle ...
A closed system may exchange heat, experience forces, and exert forces, but does not exchange matter. An open system can interact with its surroundings by exchanging both matter and energy. The physical condition of a thermodynamic system at a given time is described by its state , which can be specified by the values of a set of thermodynamic ...
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined. This local equilibrium may apply only to a certain subset of particles in the system.
[5] [6] The inversion temperature of a gas is typically much higher than room temperature; exceptions are helium, with an inversion temperature of about 40 K, and hydrogen, with an inversion temperature of about 200 K. Since the internal energy of the gas during Joule expansion is constant, cooling must be due to the conversion of internal ...