# Mechanical energy loss-thermal energy

#### Prerequisites

In previous readings, we have discussed the conservation of mechanical energy — energy that is associated with the coherent motion of an object — where all the object's molecules move together. In this case, the kinetic energy of the object (KE = ½mv2) and its momentum (p = mv) are connected through KE = p2/2m, as you can see with some simple algebra. In this case, the result of forces acting on the entire object — gravity, electricity, and springs — can be represented as potential energies and lead to a conservation theorem. Gains or losses of objects' KE is compensated by losses or gains of the PE of the objects' interactions. For this to work, the forces involved have to be conservative: they have to only depend on the objects' positions (and have to satisfy other conditions as well).

Resistive forces such as drag or friction don't satisfy those conditions and are non-conservative. They can drain the kinetic energy of our coherently moving objects in a way that makes it not obvious whether we can ever get it back. Since we know total energy is conserved, where does it go? The answer lies in thermal motion, the fact that all objects have a "hidden" internal energy due to the random motions of the atoms and molecules of which they are made. In a dilute gas, this hidden internal energy is just the kinetic energy of the molecules. In liquids and solids it includes potential energies from the interactions of the molecules as well. Since these internal kinetic and potential energies are incoherent — they correspond to zero net total momentum — in examples where we are concerned with coherent motion, it is useful to identify this internal (hidden) kinetic and potential energy as a distinct energy type — thermal energy. (In situations where we are focusing on the motion of the atoms and molecules of a substance, we may find it convenient to re-interpret thermal energy as the kinetic and potential energies that it is made of.)

Resistive forces convert the coherent mechanical energy of interacting objects into the incoherent random motions of individual molecules within the objects. In other words, when an object's KE is drained, some of its molecules are actually going faster, but they are moving randomly every which way. It's not easy to make those motions coherent again. In the follow-ons we'll study what happens to the lost energy (it is converted into thermal energy) and when it is possible to recover it as coherent macroscopic motion (free energy).

Joe Redish 8/27/13

Article 453