Energy Flow Diagrams

The study of energy flow is governed by the Principle of Conservation of Energy, which dictates that energy cannot be created or destroyed, only transformed from one form to another or transferred between systems.
In any energy transformation, the total quantity of energy remains constant throughout the process.
The mathematical expression for the conservation of energy in a closed system is represented as:
$\text{Total Energy Input} = \text{Useful Energy Output} + \text{Wasted Energy Output}$
Energy is measured in the standard unit of Joules, denoted by the symbol $J$ .

A Sankey diagram is a specialized type of flow diagram used to represent the energy transitions within a system.
The primary feature of a Sankey diagram is the use of arrows where the width of the arrow is directly proportional to the amount of energy flowing through that specific part of the system.
The layout typically follows a standard convention:
- Left-hand side: Represents the total energy input into the device or system.
- Horizontal straight arrow: Represents the useful energy output that performs the intended task.
- Diverging/Bent arrows: Usually pointing downwards or upwards, these represent the wasted energy (energy dissipated to the surroundings in non-useful forms).
Scaling in Sankey Diagrams:
- If a diagram uses a scale where $100\,J$ is represented by a width of $10\,cm$ , then $1\,cm$ of width corresponds to $10\,J$ of energy.
- Consistency in scale is mandatory to allow for accurate visual comparisons between input and output magnitudes.

Efficiency is a measure of how much of the total energy input is converted into useful energy output.
It is expressed as a decimal value between $0$ and $1$ or as a percentage between $0\%$ and $100\%$ .
The formula for calculating energy efficiency is:
$\text{Efficiency} = \frac{\text{Useful Energy Output}}{\text{Total Energy Input}}$
To convert this into a percentage, the following equation is utilized:
$\text{Percentage Efficiency} = \left( \frac{\text{Useful Energy Output}}{\text{Total Energy Input}} \right) \times 100\%$
No real-world machine or process is $100\%$ efficient; energy is always lost to the surroundings, primarily in the form of thermal energy (heat) due to friction, electrical resistance, or sound.

Filament Light Bulb:
- Input: Electrical energy.
- Useful Output: Light energy (radiation).
- Wasted Output: Thermal energy (heat radiation to the environment).
- Typical efficiency is very low, often around $5\%$ .
Electric Motor:
- Input: Electrical energy.
- Useful Output: Kinetic energy (motion).
- Wasted Output: Thermal energy (due to friction in bearings and resistance in wires) and Sound energy.
Chemical Battery and Torch:
- Transformation chain: Chemical Potential Energy $\rightarrow$ Electrical Energy $\rightarrow$ Light Energy + Thermal Energy.

Wasted energy is energy that is transferred into a form that is not intended for the device's primary function.
Thermal Dissipation: The most common form of wasted energy, where heat spreads out (dissipates) into the surroundings.
Once energy is dissipated, it becomes less useful for doing work because the energy is spread too thinly to be easily captured or utilized again.
Techniques to reduce wasted energy (improving efficiency) include:
- Lubrication: Reducing friction in mechanical systems to minimize thermal energy loss.
- Insulation: Reducing the rate of thermal energy transfer to the surroundings.
- Using low-resistance wires: Reducing heat generated in electrical circuits.