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Energy is a fundamental quantity that every physical system possesses; it allows us to predict how much work the system could be made to do, or how much heat it can exchange. Energy comes in many different forms; examples are the electrical energy stored in a battery, the chemical energy stored in a piece of food, the thermal energy of a hot heater, or the kinetic energy of a moving train. Energy can be readily transformed from one form into another; for instance, using a battery to power an electrical heater converts electrical energy into thermal energy. The law of conservation of energy states that in these conversions the total amount of energy always remains the same. This is a powerful tool in physics and, to assure its continued validity, scientists have defined several additional forms of energy that are not as easily measured by the unaided observer.
Apart from its usage in physics the concept of energy is also widely used in the many movements and beliefs that comprise New Age. In contrast to physics, its operationalization in New Age is not practical and reliable, or is even left completely undefined.
The SI unit for both energy and work is the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton-metre and, in terms of SI base units, 1 J is equal to 1 kg m2 s−2.
In cgs units, one erg is 1 g cm2 s−2, equal to 1.0×10−7 J. The imperial/US unit for both energy and work is the foot-pound, and one foot-pound is approximately 1.3558 J.
(Note that torque has the same units as energy, but there is no deeper connection between the two concepts.)
The energy unit used for everyday electricity, particularly for utility bills, is the kilowatt-hour (kW h), and one kW h is equivalent to 3.6×106 J (3600 kJ or 3.6 MJ).
An energy unit that is used in particle physics is the electronvolt (eV). One eV is equivalent to 1.602176462×10−19 J.
Main article: mechanical work.
Work is a measure of energy expended in applying force over a distance. Performing work requires energy, and thus the amount of energy in a system limits the maximum amount of work that a system could conceivably perform.
For example, in the one-dimensional case of applying a force through a distance, the energy <math>E<math> required is given by the integral:
where <math>f(x)<math> gives the amount of force being applied as a function of the distance moved, <math>x<math>.
Note, however, that not all energy in a system is stored in a recoverable form: for example, energy may be converted into heat which cannot then be converted into another useful form of energy. Thus, in practice, the amount of energy in a system available for performing work may be much less than the total amount of energy in the system.
Main article: Heat.
Heat is an amount of energy which is usually linked with a change in temperature or in a change in phase of matter. In chemistry, heat is the amount of energy which is absorbed or released by a given chemical reaction. The relationship between heat and energy is similar to that between work and energy. Heat flows from areas of high temperature to areas of low temperature. All objects (matter) have a certain amount of internal energy that is related to the random motion of their atoms or molecules. This internal energy is directly proportional to the temperature of the object. When two bodies of different temperature come in to thermal contact, they will exchange internal energy until the temperature is equalized. The amount of energy transferred is the amount of heat exchanged. It is a common misconception to confuse heat with internal energy, but there is a difference: the change of the internal energy is the heat that flows from the surroundings into the system plus the work performed by the surroundings on the system.
The first law of thermodynamics says that the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. This law is used in all branches of physics. Noether's theorem relates the conservation of energy to the time invariance of physical laws.
Main article: Kinetic energy.
Kinetic energy is the portion of energy associated with the motion of a body.
The equation above says that the kinetic energy (<math>E_k<math>) is equal to the integral of the dot product of the velocity (<math>\mathbf{v}<math>) of a body and the infinitesimal of the body's momentum (<math>\mathbf{p}<math>).
For non-relativistic velocities, we can use the Newtonian approximation
where <math>E_k<math> is kinetic energy, <math>m<math> is mass of the body, <math>v<math> is velocity of the body
At near-light velocities, we use the relativistic formula:
where <math>v<math> is the velocity of the body, <math>m<math> is its rest mass, and <math>c<math> is the speed of light in a vacuum.
The first term, <math>\gamma m c^2<math>, is the total energy of the body, and the second term, <math>m c^2<math>, is again the rest mass energy.
Main article: Potential energy.
While kinetic energy is the portion of a system's energy associated with motion, potential energy is the energy of a system associated with the spacial configuration of the system's components and their interaction(s) with each other.
In an isolated system consisting of two stationary objects lying on the x-axis that exert a force <math>f(x)<math> on each other, the potential energy is most generally defined as
where the force between the objects varies only with distance <math>x<math> and is integrated along the line connecting the two objects.
To further illustrate the relationship between force and potential energy, consider the same system of two objects situated along the x-axis. If the potential energy due to one of the objects at any point <math>x<math> is <math>U(x)<math>, then the force on the that object <math>x<math> is
This relationship demonstrates that the force between the objects is in the direction of decreasing potential energy, and the magnitude of the force is proportional to the extent to which potential energy decreases. A large force is associated with a large decrease in potential energy, while a small force is associated with a small decrease in potential energy. Notice how the force on an object depends entirely on its potential energy.
These two relationships – the definition of potential energy based on force, and the dependence of force on potential energy – show how the concepts of force and potential energy are intimately linked: if two objects do not exert forces on each other, there is no potential energy between them. If two objects do exert forces on each other, then potential energy naturally arises in the system as part of the system's total energy. Since potential energy arises from forces, any change in the system's spacial configuration will either increase or decrease the system's potential energy as the objects are repositioned.
When a system moves to a lower potential energy state, energy is either released in some form or converted into another another form of energy, such as kinetic energy. The potential energy can be "stored" as gravitational energy, elastic energy, chemical energy, rest mass energy or electrical energy, but arises in all cases from the spacial positioning and interaction of objects within a system. Unlike kinetic energy, which exists in any moving body, potential energy exists in any body which is interacting with another object.
For example a mass released above the Earth initially has potential energy resulting from the gravitational attraction of the Earth, which is transferred to kinetic energy as the gravitational force acts on the object and its potential energy is decreased as it falls.
Equation:
where <math>m<math> is the mass, <math>h<math> is the height and <math>g<math> is the value of acceleration due to gravity at the Earth's surface (see gee).
Main article: Internal energy.
Internal energy is the kinetic energy associated with the motion of molecules, and the potential energy associated with the rotational, vibrational and electric energy of atoms within molecules. Internal energy, like energy, is a quantifiable state function of a system.
In the form of a Taylor series, the relativistic formula for total energy can be written:
Hence, the third and higher terms in the series correspond with the "inaccuracy" of the Newtonian approximation for kinetic energy in relation to the relativistic formula.
An example of the conversion and conservation of energy is a pendulum. At its highest points the kinetic energy is zero and the potential gravitational energy is at its maximum. At its lowest point the kinetic energy is at its maximum and is equal to the decrease of potential energy. If one unrealistically assumes that there is no friction, the energy will be conserved and the pendulum will continue swinging forever.
Another example is a chemical explosion in which potential chemical energy is converted to kinetic energy and heat in a very short time.
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