Energy is defined as the capacity to do work or produce heat. So heat and mechanical work are two ways to exchange energy between a system and its surroundings. Work is applying force on something causing it to move, thus transferring energy by mechanical movement, heat is transferring energy by thermal interactions. They are fundamentally different: Heat is random motion of atoms that averages out to zero, while work is directed motion of atoms that does not average out to zero.

Energy cannot be created or destroyed. It can only be converted from one form to another or transferred from one system to another.

Forms of energy

Besides mass, there are two main forms of energy: kinetic and potential energy. The sum of both is described as mechanical energy.

Kinetic energy is the energy associated with an object’s motion. $$E_\text{kin}=\frac{1}{2}mv^2$$ With \(m\) the object’s mass and \(v\) its velocity.

Work is applying a force \(F\) for a distance \(d\) : \(W=Fd\) .

Potential energy is the energy of an object due to its position in a potential field. More specifically, the gravitational energy is the energy of an object due to its position in a gravitational field. (Also see the entry on gravitation.) On a planet, this is: $$E_\text{pot}=mgh$$ Where \(g\) is the gravitational acceleration (about \(9.81 m/s^2\) close to the Earth’s surface), \(m\) is the object’s mass and \(h\) is its height relative to some vertical reference point.

Internal energy \(U\) is all energy contained within a system.

Thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is the average thermal energy of a group of molecules, and heat is the transfer of thermal energy between objects. When there is a difference in temperature between two points, heat flows from high to low temperature. By convention, heat is positive if it flows into the system (increasing its energy), and negative if it is transferred from the system to the surroundings (energy loss).

A change in temperature \(T\) leads to a change in internal energy (where \(c_p\) is heat capacity, which might be a function of temperature): $$\Delta U=mc_p\Delta T$$

Chemical energy is the energy stored in bonds between atoms within molecules. It is released when those bonds are broken up, e.g. through combustion. Nuclear energy is the energy stored in nuclei.

Enthalpy

Enthalpy \(H\) is a system’s internal energy plus the amount of work required to make room for it within its surroundings: $$H=U+pV$$ At constant pressure, change in enthalpy is basically the heat gained or lost by the system. $$\Delta H= \Delta U + p\Delta V$$

Mass-energy equivalence

Mass and energy are equivalent, as described by Einstein’s formula \(E=mc^2\) , where \(E\) is the rest energy of an object and \(m\) is its mass. Since \(c\) is a large number, this means that there is a tremendous amount of energy in mass. So in a way, mass can be seen as concentrated energy.

While neutrons usually have small kinetic energies in practice, many electrons have a large kinetic energy, so it’s often necessary to use the relativistic version of Einstein’s formula for electrons, stating that the kinetic energy of a particle is the difference between its total energy and its rest mass energy: $$E=mc^2 - m_{\text{rest}}c^2$$ Where the mass \(m\) of a particle in motion increases relative to an observer at rest, depending on its speed \(v\) , according to: $$m=\frac{m_{\text{rest}}}{\sqrt{1-v²/c²}}$$

This does not apply to particles without mass, such as photons. Photons always travel at the speed of light, and their energy is \(E=hv\) , where \(v\) is the frequency of the associated electromagnetic wave, and \(h\) is Planck’s constant:

h = 4.136e-15 [eV*s]

Mass and energy can be converted into one another.

Conversion factor: 931.49 \(\text{MeV}\cdot\text{amu}^{-1}\cdot c^{-2}\)

This is the energy equivalent to 1 atomic mass unit.