Internal Energy is the energy stored in a system at the molecular Level. The System's Thermal Energy -the Kinetic Energy of the atoms due to their random motion relative to the Center of Mass plus the binding energy (Potential Energy) that holds the atoms together in terms of atomic bonds.
We consider all possible internal changes to the body as making up the total internal energy.
There are two ways to change the internal energy: with work, and everything else. Everything else is defined as heat. Heat is the defined as the transfer of energy to a body that does not involve work or those transfers of energy that occur only because of a difference in temperature. As Bellman would say,
Internal energy is one of the most important concepts in thermodynamics. Energy changes in a body sliding with friction. Warming a body increases its internal energy and cooling the body decreases its internal energy. However, what is internal energy? We can look at it in various ways: let's start with one based on the ideas of mechanics. Matter consists of atoms and molecules, and these are made up of particles having kinetic energy and potential energy. We tentatively define the internal energy of a system as the sum of the kinetic energy of all its constituent particles, plus the sum of all the potential energy of interaction among these particles.
Note that internal energy does not include potential energy arising out of interaction between the system and it surroundings. If the system is a glass of water, placing it on a high shelf, increases the gravitational potential energy arising from the interaction between the glass and the Earth. However, this has no effect on the interaction between the molecules of water, and so the internal energy of water does not change.
We use the symbol 'U' for internal energy. During a change of state of the system, the internal energy may change from an initial value U1 to a final value U2. We denote the change in internal energy as .
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