Efficiency

Efficiency is a measure of how much of the energy or power put into a system is converted into useful work or output energy. It is defined mathematically as $\eta = (Useful Output / Total Input) \times 100\%$.

Efficiency is a dimensionless quantity because it is the ratio of two identical units (Joules/Joules or Watts/Watts). It has no physical unit and is expressed either as a decimal fraction between 0 and 1, or as a percentage.

By the Conservation of Energy, the total energy input must equal the sum of the useful output work and the wasted energy: $E_{in} = E_{out} + E_{waste}$.

Frictional resistance between moving parts, aerodynamic drag (air resistance), thermal dissipation in electric coils, sound vibrations, and light reflections (in solar cells) are the main causes of energy loss.

Frictional resistance converts useful mechanical kinetic energy into thermal kinetic energy (heat). Once energy degrades into randomized heat, it cannot be fully converted back to mechanical work in a closed cycle without additional input.

In the real world, no. Frictional forces and resistive loads are always present to some degree, meaning some energy is always dissipated as non-useful heat. 100% efficiency is only achievable in idealized, frictionless systems.

No. Efficiency measures energy *conversion quality*, not speed. A highly efficient motor might lift a load very slowly using minimal power, while a less efficient, high-power motor might lift it much faster but waste a lot of energy doing so.

Since power is work done per unit time, efficiency can be calculated using rates of work: $\eta = (P_{out} / P_{in}) \times 100\%$, where $P_{out}$ is the useful output power and $P_{in}$ is the total input power.

Mechanical efficiency compares output mechanical work to input mechanical work, usually limited by friction. Electrical efficiency compares useful output (mechanical or electrical) to electrical power input, usually limited by electrical resistance ($I^2R$ losses) and electromagnetic friction.

At high speeds, aerodynamic drag increases with the square of velocity ($F_{drag} \propto v^2$), making the power required scale with the cube of velocity ($P \propto v^3$). Consequently, engines must burn fuel at a much faster rate to overcome drag, lowering distance-based fuel efficiency (mpg).

Modern commercial solar photovoltaic (PV) panels have an efficiency of around 15% to 22%. This means only about one-fifth of the solar energy hitting the panel is converted into usable electricity, while the rest is reflected or absorbed as heat.

Power plants operate on thermodynamic cycles where heat is converted to electricity. According to the Second Law of Thermodynamics, some heat must be rejected to a low-temperature sink. Cooling towers dissipate this mandatory waste heat into the atmosphere to keep the cycle running efficiently.