### 2.4 Internal energy, Energy efficiency and Power

We discuss here the concept of the Internal energy, Energy efficiency and Power.

Internal energy: "Internal energy is the capacity for doing work by virtue of the state of a system."

By definition then, internal energy cannot depend on the position neither the motion of the system. But for a given system where there are particles, we can say that the internal energy is the sum of the kinetic energy, the potential energy and the chemical energy. In case of physical systems, chemical energy is usually ignored. Another important thing to remember is that larger the system, the more the particles contained in it and hence more the internal energy. In other words, magnitude of internal energy depends on the amount of matter in a given system. for e.g Thermal energy represents an internal energy by virtue of the temperature of a system.

Here's an easy to understand video:

Energy efficiency: "It is defined as the useful energy output to the energy input."

As we have seen in the previous section the important concept of the conservation of energy. In ideal situation this conservation of energy simply imply that total energy output should be equal to the total energy input. In ordinary situation the total energy output is always less than the total energy input. Mathematically efficiency is given by the following,
$$efficiency(\eta)=\frac{E_{useful}}{E_{input}}\times 100$$
Here's a video explaning how to calculate the efficiency.

e.g. Lithium batteries only provides us 80% of the energy input during the discharge cycle. In other words the lithium batteries is only 80% efficient.

Power: "It is defined as the work done per unit time. It's SI unit is watt or joule per second $Js^{-1}$"

Mathematically, \begin{align*} P&=\frac{W}{t}\\ &=\frac{F\times d}{t} \\&=F\times v \end{align*}

where, $W=$ Work done in Joule, $F=$ Force, in $N$, and $v=$ velocity, in $ms^{-1}$

Here's a practice problem video