Thermodynamics · Quick Reference

Entropy Cheat Sheet

Thermodynamics · Lesson 10/10

In one line: 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.

Key Ideas

1What is Entropy?. A quantitative measure of the disorder, randomness, or number of possible microscopic arrangements within a system.

2The 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).

3Entropy 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.

4Microscopic 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.

5Entropy 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').

Worked Examples

200 J of heat is transferred to a system at a constant temperature of 400K (reversibly). Find the change in entropy.

0.5 J/K

Why does an ice cube melting in a warm room represent an increase in entropy?

The transition from ordered solid to disordered liquid increases the system's entropy

A gas is compressed into a smaller volume by an external force. Does the gas's entropy increase or decrease from this compression alone?

The gas's own entropy decreases (though total entropy of gas+surroundings still doesn't decrease overall)

Formulas

delta_S = Q/T (for a reversible process at constant T)

Practice Yourself

100 J of heat transfers to a system at 200K (reversibly). Find delta_S.

0.5 J/K

What does entropy measure?

The disorder or number of possible microscopic arrangements in a system

Does entropy of an isolated system ever spontaneously decrease?

No, never (it stays the same or increases)