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📘 Lesson 10 of 10 · Thermodynamics

🌀 Entropy

Entropy is one of physics' most profound ideas — a precise measure of disorder that always trends upward in isolated systems, giving time itself a natural direction.

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01 Key Concepts

What is Entropy?

A quantitative measure of the disorder, randomness, or number of possible microscopic arrangements within a system.

The Second Law in Terms of Entropy

The total entropy of an isolated system never decreases over time -- it either increases (irreversible processes) or stays constant (idealized reversible processes).

Entropy Change Formula (Simple Case)

For a reversible process at constant temperature, delta_S = Q/T, where Q is heat transferred and T is the absolute temperature.

Microscopic View of Entropy

Entropy relates to the number of ways a system's particles can be arranged while still looking the same at the macroscopic (visible) level -- more possible arrangements means higher entropy.

Entropy and the Direction of Time

Because entropy consistently increases in isolated systems, it provides a physical basis for why we experience time moving in one direction ('time's arrow').

02 Key Formulas

03 Solved Examples

Example 1 200 J of heat is transferred to a system at a constant temperature of 400K (reversibly). Find the change in entropy.
  1. Apply delta_S = Q/T = 200/400.
Answer: 0.5 J/K
Example 2 Why does an ice cube melting in a warm room represent an increase in entropy?
  1. Solid ice has a very ordered molecular structure (low entropy).
  2. Liquid water has a much more disordered, randomly arranged molecular structure (higher entropy).
  3. Melting increases the system's overall disorder.
Answer: The transition from ordered solid to disordered liquid increases the system's entropy
Example 3 A gas is compressed into a smaller volume by an external force. Does the gas's entropy increase or decrease from this compression alone?
  1. Compressing a gas into a smaller volume reduces the number of possible positions its particles can occupy.
  2. Fewer possible arrangements means lower entropy for the gas itself (though the surroundings' entropy increases due to the work done, keeping total entropy non-decreasing).
Answer: The gas's own entropy decreases (though total entropy of gas+surroundings still doesn't decrease overall)

04 Practice Questions

1100 J of heat transfers to a system at 200K (reversibly). Find delta_S.
0.5 J/K
2What does entropy measure?
The disorder or number of possible microscopic arrangements in a system
3Does entropy of an isolated system ever spontaneously decrease?
No, never (it stays the same or increases)
4Which has higher entropy: ice or liquid water (at the same mass)?
Liquid water
5What physical concept does entropy's constant increase help explain?
The directionality of time ('time's arrow')

📄 Entropy — 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