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📘 Lesson 9 of 10 · Thermodynamics

⚙️ Heat Engines

A heat engine converts thermal energy into useful mechanical work — the foundational technology behind everything from steam locomotives to modern car engines.

Course progress: 90%

01 Key Concepts

How a Heat Engine Works

Absorbs heat from a hot reservoir, converts part of it into useful work, and expels the remaining heat to a cold reservoir, typically operating in a repeating cycle.

Efficiency of a Heat Engine

Efficiency = (useful work output) / (heat input) = W/Qh, often expressed as a percentage.

The Carnot Engine

An idealized, theoretically perfect heat engine that sets the maximum possible efficiency for any engine operating between two temperatures: efficiency_max = 1 - (Tc/Th), with temperatures in Kelvin.

Why Real Engines Are Less Efficient

Friction, heat loss to the environment, and non-ideal gas behavior all reduce real engines below the theoretical Carnot efficiency limit.

The Four-Stroke Engine Cycle

A common real-world heat engine cycle: intake, compression, power (combustion), and exhaust -- repeating continuously to produce mechanical work.

02 Key Formulas

03 Solved Examples

Example 1 A heat engine absorbs 1000 J of heat and produces 300 J of useful work. Find its efficiency.
  1. Apply Efficiency = W/Qh = 300/1000.
Answer: 0.3, or 30%
Example 2 Find the maximum possible (Carnot) efficiency of an engine operating between a hot reservoir at 500K and a cold reservoir at 300K.
  1. Apply efficiency_max = 1 - (Tc/Th) = 1 - (300/500).
  2. = 1 - 0.6.
Answer: 0.4, or 40%
Example 3 Why can no real engine achieve 100% Carnot efficiency, even in theory?
  1. Carnot efficiency = 1 - (Tc/Th) only equals 1 if Tc=0 (absolute zero).
  2. Since absolute zero can never actually be reached, some heat must always be expelled to a nonzero-temperature cold reservoir.
Answer: Because a cold reservoir at absolute zero (Tc=0) is physically unattainable

04 Practice Questions

1A heat engine absorbs 500 J and produces 150 J of work. Find its efficiency.
0.3 or 30%
2Find the Carnot efficiency between Th=600K and Tc=300K.
1-(300/600)=0.5 or 50%
3What does a heat engine's efficiency measure?
The fraction of absorbed heat converted into useful work
4Why is a Carnot engine considered an idealized, unrealistic engine?
It assumes perfectly reversible processes with no friction or other losses, which doesn't occur in real machines
5What are the four strokes of a typical car engine cycle?
Intake, compression, power, and exhaust

📄 Heat Engines — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet