Energy

From the perspective of physics, every physical system contains (alternatively, stores) a quantity called energy; exactly how much is determined by taking the sum of a number of special-purpose equations, each designed to quantify energy stored in a particular way. There is no uniform way to visualize energy; it is best regarded as an abstract quantity useful in making predictions.

The first sort of prediction energy allows one to make is how much work a physical system could be made to do. 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. In the one-dimensional case of applying a force through a distance, the energy required is ∫ f(x) dx, where f(x) gives the amount of force being applied as a function of the distance moved.

Note, however, that not all energy in a system is stored in a recoverable form; 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.

Energy also allows one to make predictions across problem domains. For example, if we assume we are in a closed system (i.e. the conservation of energy applies), we can predict how fast a particular resting body would be made to move if a particular amount of heat were completely transformed into motion in that body. Similarly, it allows us to predict how much heat might result from breaking particular chemical bonds.

The SI unit for both energy and work is the joule (J), named in honor 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 equals 1 kg m2/s2. (Conversions. In cgs units, one erg is 1 g cm2/s2. The imperial/US unit for both energy and work is the foot pound.)

Noether's theorem relates the conservation of energy to the time invariance of physical laws.

Energy is said to exist in a variety of forms, each of which corresponds to a separate energy equation. Some of the more common forms of energy are listed below.

Kinetic energy

Kinetic energy is that portion of energy associated with the motion of a body.

Ek = ∫ v·dp

For non-relativistic velocities, we can use the Newtonian approximation

Ek = 1/2 mv2

(where Ek is kinetic energy, m is mass of the body, v is velocity of the body)

At near-light velocities, we use the relativistic formula:

Ek = moc2(γ - 1) = γmoc2 - oc2 :γ = (1 - (v/c)2)-1/2

(where v is the velocity of the body, mo is its rest mass, and c is the speed of light in a vacuum.)

The second term, mc2, is the rest mass energy and the first term, γmc2 is the total energy of the body.

Heat

Heat is related to the internal kinetic energy of a mass, but it is not a form of energy. Heat is more akin to work in that it is a change in energy. The energy that heat represents a change specifically refers to the energy associated with the random translational motion of atoms and molecules in some identifiable mass. The conservation of heat and work form the First law of thermodynamics.

Potential energy

Potential energy is energy associated with being able to move to a lower-energy state, releasing energy in some form. For example a mass released above the Earth has energy resulting from the gravitational attraction of the Earth which is transferred in to kinetic energy.

Equation:

Ep=mhg

where m is the mass, h is the height and g is the value of acceleration due to gravity at the Earth's surface.

Chemical energy

Chemical energy a form of potential energy related to the breaking and forming of chemical bonds.

Mass

In the theory of relativity, the energy E of a particle is related to its momentum p and mass m by:

E2 = m2c4 + p2c2

where c is the speed of light. This equation shows that the mass provides a contribution to the energy. Even if p is zero, the particle has a rest energy that is nonzero if the mass is nonzero. The rest energy is

E0 = mc2 (i.e. 90 petajoule/kg)