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The terms 'heat' and 'energy' are often used interchangeably, but in fact they are not synonymous. Heat refers to a transfer of energy from one substance to another. This happens on an atomic level, so we have no mean to feel it directly, but only by an indirect measure. The 'energy level' of one body in respect to another tell us in which direction energy flows. This level is known as temperature.

Internal energy is the energy that a subsyance or body possesses at a certain temperature. We know that particle of a gas (atoms or molecules) are in motion, thus giving rise to kinetic energy. Pressure is the practical consequence of this. In a liquid this motion is present, however intermolecular attractions bind particles this limiting they freedom of movement.

Even in a solid particles have kinetic energy, but the movements are restricted to oscillations of atoms or molecular fragments around a center. So internal energy maybe quite high, even for a standing object, like a glass of water on a table.

For one mole of an ideal monoatomic gas (i.e. 6.022*1023 particles) the remarkable result of thermodynamics ia that the internal energy of this amoun of matter is :

E = 3/2 * R * T

where R is the universal gas constant , 8.314 J/mol/K and T is the absolute temperature (in Kelvin)

Internal energy of a substance different from an ideal monoatomic gas has unfortunately no such simple expression. Interatomic forces, chemical bonds, and intermolecular interactions make things much more difficult.

Imagine a piece of matter, made up by a number of atoms. Imagine to create it at a temperature of zero kelvin, where thermal motion is null. By direct union of the constituents atoms we form chemical bonding. In this spontaneous process energy is released and transferred to the sorrounding, so at its end the process the internal energy of the body is lower to some extent in respect to starting situation (free atoms). Electrostatic interactions in chemical bonds give now structure and stenght to the substance; if we wish to break them out, the same amount of energy has to be given.

If we are not at zero kelvin, we must consider the 'thermal movement' contribution, that accounts for the energy of atomic oscillation and translation, in other words, heating up the body for example from 0 K to 298 K (25°C) we have to supply energy from the sorrounding. Moreover our system has a finite volume, so expanding it (making room for it) we must supply an expansion work.



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