# Law of conservation of energy

The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. This means that a system always has the same amount of energy, unless it's added from the outside. This is particularly confusing in the case of non-conservative forces, where energy is converted from mechanical energy into thermal energy, but the overall energy does remain the same. The only way to use energy is to transform energy from one form to another.

The amount of energy in any system, then, is determined by the following equation:

$U_{T} = U_{i} + W + Q$

• $U_T$ is the total internal energy of a system.
• $U_i$ is the initial internal energy of a system.
• $W$ is the work done by or on the system.
• $Q$ is the heat added to, or removed from, the system.

It is also possible to determine the change in internal energy of the system using the equation: $\Delta U = W + Q$

This is also a statement of the first law of thermodynamics.

While these equations are extremely powerful, they can make it hard to see the power of the statement. The takeaway message is that energy cannot be created from nothing. Society has to get energy from somewhere, although there are many sneaky places to get it from (some sources are fuels and some sources are flows).

Early in the 20th century, Einstein figured out that even mass is a form of energy (this is called mass-energy equivalence). The amount of mass directly relates to the amount of energy, as determined by the most famous formula in physics:

$E = mc^{2}$

• $E$ is the amount of energy in an object or system.
• $m$ is the mass of the object or system.
• $c$ is the speed of light, roughly $3\times10^8 m/s$.