Energy is defined as the ability to do work and is a fundamental concept in almost all areas of science.
The SI unit for Energy is the same as for work, the Joule (J), which corresponds to 1 kg m2/s2. Energy can exist in a variety of forms. Some of the more common forms of energy are listed below:
Kinetic energy is that portion of energy associated with the motion of a body.
KE = ∫ v·dp
For non-relativistic velocities, we can use the Newtonian approximation
KE = 1/2mv2 (where KE is kinetic energy, m is mass of the body, v is velocity of the body)
At near-light velocities, we use the relativistic formula:
KE = moc2(γ - 1) = γmoc2 - moc2 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 is a form of Kinetic energy. It specifically refers to the energy associated with the random translational motion of atoms and molecules. The conservation of heat and work form the First law of thermodynamics.
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.
Chemical energy a form of potential energy related to the breaking and forming of chemical bonds.
Mass can also be considered a form of energy. This is demonstrated by Einstein's famous equation:
E = moc2 (Where e = energy and c = the speed of light)
showing that energy is proportional to mass. However it is not practically possible to convert all of matter in to energy now or in the near future.