use the concept of efficiency to solve problems

Energy Conservation ⚡️

Energy conservation means that the total energy in a closed system stays constant. It’s like a big, invisible “energy bank” that never loses money, only changes form.

What is Energy?

Energy is the ability to do work. It comes in many forms: kinetic, potential, thermal, electrical, chemical, etc.

Why is Conservation Important?

• It lets us predict how systems behave.
• It helps design efficient machines.
• It explains why some energy is “lost” as heat.

Efficiency 🏗️

Definition

Efficiency, denoted by $η$, is the ratio of useful output energy to input energy:

$$η = \\frac{E_{out}}{E_{in}}$$

It is usually expressed as a percentage: $η\\% = η \\times 100$.

Analogy

Think of a water pump. If you pour 10 litres of water into the pump but only 7 litres come out, the pump’s efficiency is 70 %.

Solving Problems with Efficiency ⚙️

Step‑by‑Step Guide

1. Identify the input energy ($E_{in}$).
2. Identify the useful output energy ($E_{out}$).
3. Insert into $η = \\frac{E_{out}}{E_{in}}$.
4. Calculate $η$ and convert to a percentage if required.
5. Check if the result makes sense (e.g., $0\\leq η\\leq1$).

Example Problem

⚡️ A light bulb receives 100 J of electrical energy. Only 60 J is converted into visible light; the rest becomes heat.

What is the bulb’s efficiency?

?? The bulb is 60 % efficient. The remaining 40 % is lost as heat.

Common Mistakes to Avoid ❌

• Mixing units – always use the same units for $E_{in}$ and $E_{out}$.
• Forgetting that $η$ is a fraction, not a percentage, until you multiply by 100.
• Assuming $η$ can be greater than 1 – that would mean you created energy!

Quick Quiz 🧠

1. A car engine uses 200 kJ of fuel energy and delivers 120 kJ of mechanical work. What is the engine’s efficiency?
2. If a solar panel receives 500 W of sunlight and outputs 350 W of electricity, what is its efficiency?

Answers:

• Efficiency = $\\frac{120}{200}=0.60\\;\\text{or}\\;60\\%$.
• Efficiency = $\\frac{350}{500}=0.70\\;\\text{or}\\;70\\%$.

Take‑Away Points 📌

• Energy is conserved, but its form can change.
• Efficiency tells us how well a device uses the energy it receives.
• Always check units and remember $0\\leq η\\leq1$.