Internal energy

The internal energy of a system is given by the sum of the kinetic energy and the potential energy. This excludes the external energy of the system, for example motion of the center of mass of the system, or the presence of an external field.

The internal energy in classical thermodynamics is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. U \right.=TS-pV}

and in statistical mechanics by

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where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is the Helmholtz energy function and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} is the partition function.