In thermodynamics, internal energy, symbol U, or energy, symbol E, as is synonymously used, of a body, is a state variable that expresses the sum of the increment of the heat actually existing in a body in the form of kinetic energy (vis viva or molecular motion) and of the heat consumed in internal work, when the body changes, from a given initial state reference point, due to the addition of an amount of heat Q imparted to the body, quantified by the formula: [1]

where H is the “quantity of heat” actually existing in a body, i.e. the vis viva of its molecular motions, and J is the ergal or heat consumed in doing internal work, the work which the internal forces performed, while the body was passing from any given initial condition, taken as a starting point, to its condition at the moment under consideration.

The internal energy is path independent, that is it depends only on the condition of the body at the moment, and not on the way in which it arrived at that condition. [2]

History
The expression for internal energy was defined in 1850 by German physicist Rudolf Clausius.

In 1875, Clausius compared his U function to similar variations given by other authors on the subject of heat: Scottish physicist William Thomson (1851) calls it the “mechanical energy of a body in a given state”, German physicist Gustav Kirchhoff calls it “function of activity” (wirkungsfunction), and German physicist Gustav Zeuner calls it “interior heat” (1860) of the body as well as “internal work” (1866) of the body. [2]

References
1. Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws Which can be Deduced From it for the Theory of Heat." Poggendorff's Annalen der Physik, LXXIX, 368, 500.
2. Clausius, Rudolf. (1879). The Mechanical Theory of Heat, (pgs. 31-32). London: Macmillan & Co.