In mechanics, energy is sometimes defined as “the capacity-for-doing-work” of a system. This “mechanical energy”, is not the same thing as the energy of thermodynamics, although the two concepts have features in common.
In thermodynamics energy is defined as The increase of energy of a system during a change of state is numerically equal to the net heat (Q) during the process minus the net work during the process. In symbols this definition is written as:
E2 – E1 ≡ Q − W
where E2 and E1 are the energies of the system in the final state 2 and the initial state 1 respectively.
The ball in the bowl
If a system is any prescribed and identifiable collection of matter, then imagine the ball in the bowl as shown in picture below:
Suppose that initially the ball is at rest at the lowest point of the bowl, and that then it is raised by an external force (for example a hand) until it is at rest near the rim, in doing so what is happening is the work is done by the system. This work is said to be negative in the process (moving the ball from rest at the lowest point & resting it near the rim) since the surroundings have done work on the system; heat transfer being absent, then definition of energy becomes
E2 – E1 ≡ Q − W
E2 – E1 ≡ 0 − (−W)
E2 – E1 ≡ +W i.e. the energy of the system increases.
& the “mechanical energy” has also increased, & indeed by the same amount, for the ball is higher than it was.
Now suppose that the ball is released so that it rolls back wards and forwards within the bowl. Since there are neither heat nor work interactions at the boundary of the system during the oscillations, it is seen from E2 – E1 ≡ Q − W there can be no change of energy.
If friction ignored:
the decrease of gravitational potential energy which the ball suffers in reaching the bottom of the bowl is exactly balanced by its increase in kinetic energy: the sum of the two energy terms remains constant.
No change in “mechanical energy” for the system
If friction is present:
the height reached by the ball in each successive oscillation is reduced; the maximum velocity attained is also lower at each oscillation. Finally the ball comes to rest again in the bottom of the bowl. Since still no heat or work interactions are present at the system boundary, the energy of the system has the same value as immediately after the ball was first raised.
The “mechanical energy” however has decreased to the value prevailing before the ball was first raised. In mechanics it is said that “the energy has been dissipated”. An alternative phrase used in mechanics is: “the energy has been converted into heat”. This phrase is NOT in accordance with thermodynamic usage of the word “heat”; for, although the ball and the bowl no doubt have a higher temperature than in the beginning, this has not been accomplished by heat transfer between the system and its surroundings.
Energy is seen to include the energy which is defined in mechanics, but to be more general than it. For example, it covers internal energy also. Processes may occur in which the energy of the system remains constant, but change occur from one form of mechanical energy to another and from mechanical to internal energy.
“capacity-for-doing-work” idea plays an important part in more advanced thermodynamic it forms the core of the concept of “availability”.
Qualitatively some of the other forms of energy.
A system may change its chemical state, as for example when Petrol (gasoline) & air react so as to form carbon dioxide, water vapour & other combustion products. Often, if the system is isolated from its surroundings as regards heat & work, the temperature of the system changes greatly as a result of such a chemical-reaction process: in the Petrol (gasoline)-air case the temperature increases. It is sometimes helpful to regard such processes, which are at constant energy as involving a changing of “chemical energy” into internal energy.
A compressed spring or elastic structure may be regarded as having part of its energy in the form of “strain energy”.
A related form of energy is that associated with the phenomenon of capillarity, or surface tension; systems exhibiting this phenomenon may be said to have part of their energy in the form of “surface energy”.
A system comprising electrically charged elements may be considered, by reason of the attractions & repulsions existing between these elements, to have part of its energy in the form of “electrical energy”. “Magnetic energy” correspondingly is present if the system comprises magnetic poles.