Welcome to the World of Efficiency!
Have you ever noticed that a phone charger gets warm after being plugged in, or that an old-fashioned lightbulb is too hot to touch? This happens because no machine is perfect. In Physics, we want to know exactly how much energy a device actually "uses" for its job compared to how much it "wastes." This is what Efficiency is all about!
In this chapter, we will learn how to calculate efficiency and how to draw Sankey Diagrams to visualize energy transfers. This is a core part of the "Energy resources and energy transfers" section of your Edexcel IGCSE.
1. What is Efficiency?
Efficiency is a way of describing how good a device is at transferring energy into the form we actually want.
According to the Principle of Conservation of Energy, energy cannot be created or destroyed—it can only be transferred from one store to another. However, not all transfers are "useful."
Useful Energy: Energy transferred to the store where it is wanted (e.g., light from a bulb).
Wasted Energy: Energy transferred to a store that is not useful (e.g., thermal energy heating up the surroundings).
The Efficiency Formula
To find the efficiency of a device, we use this formula (which you need to memorize!):
\( \text{efficiency} = \frac{\text{useful energy output}}{\text{total energy output}} \times 100\% \)
Note: You can also express efficiency as a decimal between \( 0 \) and \( 1 \). For example, \( 0.75 \) is the same as \( 75\% \). However, most exam questions ask for the percentage.
Example: A radio transfers \( 50\text{ J} \) of electrical energy into \( 10\text{ J} \) of sound energy and \( 40\text{ J} \) of thermal energy.
The useful energy is the sound (\( 10\text{ J} \)).
The total energy is \( 50\text{ J} \).
\( \text{efficiency} = \frac{10}{50} \times 100 = 20\% \)
Key Takeaway:
Efficiency can never be greater than \( 100\% \). If your calculation gives you a number bigger than \( 100 \), you have likely put the "total energy" on top of the fraction by mistake! Always put the smaller number (useful) over the bigger number (total).
2. Sankey Diagrams
A Sankey Diagram is a visual way to show energy transfers. It looks like a thick arrow that splits into smaller branches.
How to read a Sankey Diagram:
1. The Width Matters: The most important rule is that the width of the arrow represents the amount of energy in Joules (\( J \)). A wider arrow means more energy.
2. The Input: The total energy entering the system is shown by the thickness of the arrow on the far left.
3. Useful Output: This is shown by the arrow pointing straight ahead.
4. Wasted Output: This is shown by the arrow(s) curving downwards (usually representing thermal energy dissipated to the surroundings).
Conservation in Diagrams
Because energy is conserved, the total width of the input must equal the sum of the widths of the output arrows.
\( \text{Total Energy In} = \text{Useful Energy Out} + \text{Wasted Energy Out} \)
Quick Tip:
In exams, you might be given a grid. If the input arrow is \( 10 \) squares wide and represents \( 100\text{ J} \), then each single square of width represents \( 10\text{ J} \). Always check the scale!
3. Step-by-Step: Solving Efficiency Problems
Don't worry if these calculations feel confusing at first. Just follow these steps:
Step 1: Identify the Total Energy Input. This is the energy the device starts with (e.g., electricity from the plug).
Step 2: Identify the Useful Energy Output. What is the device designed to do? (e.g., a motor's job is kinetic energy).
Step 3: Use the formula. Divide the useful by the total.
Step 4: Multiply by \( 100 \). This turns your decimal into a percentage.
Step 5: Units. Remember that energy is measured in Joules (\( J \)), but efficiency itself is a percentage (\( \% \)) or a ratio (no units).
"Did you know?"
Modern LED lightbulbs are much more efficient than old filament bulbs. An LED might be \( 90\% \) efficient (meaning only \( 10\% \) is wasted as heat), whereas an old bulb might be only \( 10\% \) efficient (wasting \( 90\% \) as heat!).
4. Common Pitfalls to Avoid
Mistake: Forgetting that "work done" is the same as "energy transferred."
Fix: If a question gives you "work done" in Joules, use it exactly like you would use an energy value in your efficiency formula.
Mistake: Confusing Power and Energy.
Fix: While efficiency is usually calculated with Energy (\( J \)), it can also be calculated using Power (\( W \)). The formula stays the same: \( \text{efficiency} = \frac{\text{useful power output}}{\text{total power input}} \times 100\% \).
Mistake: Drawing Sankey arrows with points that don't match the width.
Fix: When drawing, ensure the rectangular body of the arrow is the correct width according to the scale. The pointy tip of the arrow doesn't count towards the energy width!
Summary Review
- Efficiency measures how much energy is usefully transferred.
- Formula: \( \frac{\text{useful}}{\text{total}} \times 100\% \).
- Sankey Diagrams: Width represents energy; useful goes forward; wasted goes down.
- Conservation: Input width \( = \) sum of output widths.
- Units: Energy is in Joules (\( J \)); Efficiency is a \( \% \).