Energy
Energy and Thermal Physics

## Energy of a system

Glossary Definition for 16-19

#### Description

The energy of a system that is completely isolated is a quantity that is conserved: it cannot change and is therefore useful in making numerical calculations.

When using the conservation of energy in calculations, it is important to identify an appropriate starting state and an end state for the process to be analysed.

In most circumstances, systems are not isolated and energy can be transferred into or out of them. There are two ways this can happen. One is if the system does some work, or has some work done on it. As an example, we can change the energy of a spring by stretching it. The other way in which the energy of a system can change is if its temperature is different from that of its surroundings. In that case, energy will be transferred from the hotter entity (the system or its surroundings) to the cooler one. This process is referred to as heating.

The energy of a closed system can be split into a kinetic energy, due to its bulk motion, and an internal energy, due to the motion of its constituent parts and the interactions between them. Those interactions – and the relative positions of the constituents – give rise to a term for potential energy that is part of the internal energy of the system.

Energy is usually represented by the symbol E.

#### Discussion

The conservation of energy is a very powerful tool for doing calculations. However, it is very important to define carefully what the system is. Consider a ball falling towards the floor; there is a force acting on the ball due to the Earth, and an equal force acting on the Earth due to the ball. The interaction between the ball and the Earth has an associated energy, so it makes sense to define the system in this case as the combination of the Earth and the ball. Within that system, energy is conserved. This condition means that as the ball gets closer to the floor, that is, the separation between the ball and the Earth decreases, the potential energy of the system decreases so its kinetic energy must increase. In this case, because the Earth’s mass is so much greater than the ball’s, the Earth’s acceleration is effectively zero, and almost all the additional kinetic energy is with the ball, which therefore speeds up as it falls.

joule, J

kg m2  s–2

none

#### Mathematical expressions

• ΔE = W + Q
where ΔE is the change in the internal energy of the system due to W, the work done on it and to Q, the energy transferred to the system by heating.

#### Related entries

• Force
• Heat
• Internal energy
• Kinetic energy
• Potential energy
• Power
• Specific heat capacity
• Work

#### In context

We often use electrical heaters to raise the temperature of a room. The way we do this is for the power station, via the electricity transmission network, to do some electrical work on the element of the heater, which raises its temperature well above room temperature. As a result, the element transfers energy, by heating, to the surrounding air to raise its temperature. To raise the temperature of a small room by 5 °C requires about 100 kJ of energy, or about 2 minutes of a 1 kW electric heater, although in practice, the air in the room will also heat other objects in contact with it, so that this time will be longer. In this scenario it may be useful to consider either the electrical heater element alone, or the electrical heater together with the air in the room, to be the system under discussion

###### Energy
appears in the relation ΔEΔt>ℏ/2 ΔQ=mcΔθ E=hf E ∝ A^2
has the special case Photon Energy
is used in analyses relating to Emission/Absorption Spectra Phase Change