1.1.1 Einstein’s equation

Energy can take many forms and may be transformed from one form to another. For example, a projectile has kinetic energy arising from its speed, a hot object has thermal energy due to its temperature and an object on a ledge of a high cliff has potential energy by virtue of its position.

At the beginning of the century, in his Theory of Relativity, Albert Einstein showed that mass is also a form of energy. Mass may therefore be regarded as analogous to the parameters’ speed, temperature and height in the foregoing examples. Increasing any of these parameters requires energy to be supplied where­as a decrease leads to the spontaneous and inevitable release of the equivalent amount of energy Table 1.1.

Referring to Table 1.1, take as an example an elec­tric kettle containing water at temperature ti say. To increase the temperature to a higher value іг electrical energy must be supplied [s ms(t2 — ti) where m is the mass of water and s specific heat]. But hot water at t2 will spontaneously cool down to a lower tem­perature 11, the heat energy in this case being released to the surrounding atmosphere. In his theory Einstein derived the equation ДЕ = С2Дт where Дт is the change in mass and ДЕ the equivalent energy. He then postulated that all mass could be converted into energy and wrote his now familiar equation E = m C2 where the constant of proportionality C2 is the square of the speed of light in vacuo. Now C = 3 x 108 m/s and hence the energy associated with a very small change in mass is very large indeed. This is why the mass changes which occur in, for example, chemical reactions — like burning a fuel — are not normally detectable.