To find out how well a heat engine works, we need to understand what "efficiency" means.

In simple terms, efficiency tells us how good a machine is at turning the energy it uses into useful work.

For heat engines, this means changing heat energy into mechanical work.

How to Calculate Efficiency

We can figure out a heat engine's efficiency (which we can call $\eta$) by using this formula:

$$\eta = \frac{\text{Work Output}}{\text{Heat Input}} \times 100\%$$

Here’s what the terms mean:

• Work Output: This is how much useful work the engine actually does.
• Heat Input: This is the heat energy the engine gets from a heat source.

Example

Let’s say we have a steam engine that takes in 2000 J (joules) of thermal energy and does 800 J of useful work.

We can calculate its efficiency like this:

1. Identify Values:

   • Heat Input: 2000 J
   • Work Output: 800 J

2. Use the Formula:

$$\eta = \frac{800 \text{ J}}{2000 \text{ J}} \times 100\% = 40\%$$

This means the engine has an efficiency of 40%.

It successfully converts 40% of the heat energy into useful work.

The remaining 60% usually gets lost as waste heat.