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?

Energy TypeEnergy (J)
Input (electrical)100
Output (visible light)60
Efficiency\$\\frac{60}{100}=0.60\\;\\text{or}\\;60\\%\$

??

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\$.