10. Efficiency | Energy & Power

1. What is Efficiency?

Definition

• Concept: Efficiency is the proportion of the total energy (or power) supplied to a device that is actually transferred into a useful form.

• Useful vs. Wasted Energy: * Useful: The energy transferred for the device's intended purpose (e.g., light from a lamp).

  • Wasted: Energy transferred into non-useful forms, most commonly thermal energy (heat).

• Energy Conservation: No device can be more than 100% efficient, as energy cannot be created, only transferred.

2. Calculating Efficiency

The Equations

Efficiency can be calculated using either energy or power:

1. Efficiency = Useful Energy Output / Total Energy Input

2. Efficiency = Useful Power Output / Total Power Input

Representing Efficiency

• Decimals: Efficiency is often expressed as a value between 0 and 1.

• Percentages: To convert a decimal to a percentage, multiply by 100 (e.g., 0.75 = 75%).

• Rearranging: If you have the efficiency and the total input, you can find the useful output: Useful Output = Efficiency × Total Input.

3. Practical Examples and Calculations

Comparing Light Bulbs (Energy)

• Incandescent Bulb: If it takes in 300 J and outputs 45 J of light, efficiency is 45 / 300 = 0.15 (15%).

• LED Bulb: If it takes in 300 J and outputs 225 J of light, efficiency is 225 / 300 = 0.75 (75%).

• Comparison: The LED bulb is 5 times more efficient than the incandescent bulb (0.75 ÷ 0.15 = 5).

Microwave Calculation (Power)

• Problem: A microwave is 70% efficient with an 800 W total power input.

• Step 1: Convert 70% to a decimal (0.7).

• Step 2: Multiply efficiency by total input (0.7 × 800 W).

• Result: The useful power output is 560 W.

4. Key Considerations

Avoiding Common Errors

• The "Check": If your calculation results in a value greater than 1 or 100%, you have likely divided the numbers the wrong way around. A device cannot output more energy than it receives.

Exceptions to Wasted Energy

• Heat as a Purpose: Most devices consider heat to be wasted energy. However, for devices designed specifically to produce heat (like electric heaters), the thermal energy produced is considered useful output. This is one of the few cases where a device can approach 100% efficiency.

5. Summary Table