Thermal Energy
Although a body at rest relative to a reference frame has zero kinetic energy relative to that reference frame it still maintains an energy of motion known as thermal energy.
The essential concepts underlying thermal energy predate Newtonian physics. A generation before Isaac Newton, the English natural philosopher Robert Boyle conjectured that heat might be associated with the motion of the individual atoms that constitute matter.
A body's thermal energy is that which is due to the random motion of its constituent atoms or molecules. They are constantly moving in all directions or vibrating at varying speeds or frequencies. If, for moving particles, we were to sum up the individual velocity vectors, we would, on average, obtain zero; for every particle moving in a particular direction with a specific speed, there is another moving at the same speed, but in the direction opposite. But if we were to square each velocity vector and then sum, so that all the terms were positive, we would, of course, find a nonzero result. Such a sum (with each term multiplied by the individual particle's mass) is a measure of the body's internal kinetic or thermal energy.
As a ball falls from a height relative to a particular reference frame (e.g., the ground), its gravitational potential energy, (which it possesses by virtue of its mass, height, and the acceleration due to gravity), is converted into kinetic energy, (which it possesses by virtue of its mass and velocity. Its speed increases as its height decreases. Energy is being conserved. When the ball strikes the ground the ball (assuming it does not bounce) stops, and accordingly, its kinetic energy goes to zero. Ignoring other factors, the KE is transformed into thermal energy. The ball's constituent particles, however, move or oscillate faster than before the collision. The kinetic energy is thus converted into thermal energy, and increases the ball's temperature.
Mechanical energy can be converted into thermal energy and thermal energy into mechanical energy. The laws of energy conservation, however, place an important limitation on such transformations. A body containing a certain amount of thermal energy, as measured indirectly by temperature, is able to perform a certain amount of work on another object or system. Indeed, these types of transformations are typical in many types of engines. The transformation into work, however, is limited by the second law of thermodynamics. An thermal engine will utilize the thermal energy in a hotter body or reservoir and then transform a fraction (called the engine's "efficiency") of that thermal energy into mechanical work and utilizing the remainder to heat the cooler body until both systems are in thermal equilibrium. In such processes, a small amount of thermal energy is utilized toward the required increase in entropy. As work is done by the engine, the hotter body cools, and the cooler body heats up. When they achieve the same temperature no, more work can be done.
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