4.1.2.1 Energy Transfers in a System

In Physics, the behavior of energy is governed by one of the most fundamental laws in the universe: the Law of Conservation of Energy. Understanding how energy moves—and why some of it is "lost"—is key to mastering this topic.

1. The Law of Conservation of Energy

The Law of Conservation of Energy states:

Energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed.

This means that for any system, the total amount of energy before a change is exactly the same as the total amount of energy after the change.

In a closed system, where no energy can enter or leave to the surroundings, the total energy remains constant regardless of the transfers happening inside.

2. Useful vs. Dissipated Energy

When energy is transferred, it is rarely 100% efficient. Energy is usually split into two categories:

1. Useful Energy: Energy transferred to the store where it is wanted (e.g., light from a lightbulb).
2. Dissipated Energy: Often called "wasted" energy. This is energy that is spread out into the surroundings, usually in the form of thermal energy, making the surroundings warmer. Once energy is dissipated, it can no longer be used for a useful purpose.

3. Examples of Energy Transfers

To describe an energy transfer, you must identify the initial store, the transfer pathway, and the final stores.

4. Reducing Energy Waste

A common exam question asks how to reduce the dissipation of energy. There are two primary methods:

1. Lubrication: In mechanical systems (like a bike chain), friction causes energy to be dissipated as heat. Applying oil or grease reduces friction, so less energy is wasted as thermal energy.
2. Thermal Insulation: In heating systems (like a house), energy is dissipated to the surroundings. Using materials with low thermal conductivity (insulation) reduces the rate at which energy is transferred away.

5. Edge Cases & Common Misconceptions

The "Disappearing" Energy: Students often say energy is "lost." In physics, energy is never lost; it is dissipated to the surroundings. Use the word "dissipated" or "wasted" to gain full marks.

Friction in a Vacuum: If there were no air resistance or friction (an ideal system), 100% of Gravitational Potential Energy would transfer to Kinetic Energy. In reality, some is always dissipated as thermal energy due to air particles.

Mathematical Example: Conservation in Action

A motor transfers $500\text{ J}$ of energy from its chemical store. It transfers $200\text{ J}$ usefully to lift a weight (Gravitational Potential store). Calculate the amount of energy dissipated to the surroundings.

Calculation:

Total Energy In = Total Energy Out

$500\text{ J}=200\text{ J (Useful)}+\text{Dissipated Energy}$

$\text{Dissipated Energy}=500\text{ J}-200\text{ J}=300\text{ J}$

4.1.2.2 Efficiency

Efficiency is a measure of how much of the total energy supplied to a device is transferred into useful energy stores. The higher the efficiency, the less energy is wasted (dissipated) to the surroundings.

1. The Efficiency Formulas

You can calculate efficiency using either energy or power. Because efficiency is a ratio, it has no units, though it is often expressed as a percentage.

Calculation using Energy:

$\text{Efficiency}=\frac{\text{useful output energy transfer}}{\text{total input energy transfer}}$

Calculation using Power:

$\text{Efficiency}=\frac{\text{useful power output}}{\text{total power input}}$

Note: To get a percentage, simply multiply the result by 100.

2. Representing Efficiency: Sankey Diagrams

Sankey diagrams show the "flow" of energy through a system.

1. The width of the arrows represents the amount of energy.
2. The horizontal arrow usually represents the useful energy.
3. The downward-pointing arrow represents the wasted (dissipated) energy.

3. Improving Efficiency

In the AQA exam, you may be asked how to increase the efficiency of a system. The goal is to reduce the energy dissipated to the surroundings.

1. Mechanical Systems: Use lubrication (like oil) to reduce friction between moving parts, which minimizes energy wasted as thermal energy.
2. Thermal Systems: Use insulation to reduce the rate at which heat is lost to the surroundings.
3. Electrical Systems: Use low-resistance wires to reduce the heating effect as current flows through a circuit.

4. Edge Cases and Rules

1. The 100% Rule: No device is 100% efficient. Some energy is always dissipated to the thermal store of the surroundings. (The only exception is an electric heater, where "wasted" thermal energy is actually the useful output).
2. The "1" Limit: If you calculate efficiency and get a number greater than 1 (or 100%), you have likely swapped the input and output values! The output can never be greater than the input.

5. Mathematical Examples

Example 1: Energy Efficiency

An electric motor is supplied with 2000 J of energy. It usefully transfers 1500 J to lift a load. Calculate the efficiency.

Step 1: Identify values

1. Useful output = 1500 J
2. Total input = 2000 J

Step 2: Calculate

$\text{Efficiency}=\frac{1500}{2000}=0.75$

Percentage Efficiency: $0.75\times 100=75\%$

Example 2: Finding Total Input

A lightbulb has an efficiency of 0.2 (20%). If it produces 10J of useful light energy, how much total energy was supplied to it?

Step 1: Rearrange the formula

$\text{Total input}=\frac{\text{useful output}}{\text{efficiency}}$

Step 2: Calculate

$\text{Total input}=\frac{10}{0.2}=50\text{ J}$