Entropy Change Formula
The entropy change formula calculates disorder change in thermodynamic processes using the second law.
Learn with examples.
The Formula
The entropy change formula calculates how the entropy of a system changes when heat is added or removed at a constant temperature. Entropy is a measure of the number of microscopic arrangements (microstates) available to a system.
The concept of entropy was introduced by German physicist Rudolf Clausius in 1865. The second law of thermodynamics states that the total entropy of an isolated system can only increase or stay the same, never decrease. This is why heat flows spontaneously from hot to cold, and why many processes are irreversible.
For reversible processes at constant temperature, ΔS = Q/T gives the exact entropy change. For processes where temperature varies, you must integrate: ΔS = ∫ dQ/T. The units of entropy are joules per kelvin (J/K).
Variables
| Symbol | Meaning |
|---|---|
| ΔS | Change in entropy (joules per kelvin, J/K) |
| Q | Heat transferred to the system (joules, J) |
| T | Absolute temperature during the transfer (kelvin, K) |
Example 1
An ice cube absorbs 3,340 J of heat while melting at 0°C (273 K). What is the entropy change?
Given: Q = 3,340 J, T = 273 K
Apply the formula: ΔS = Q/T = 3,340 / 273
ΔS ≈ 12.23 J/K (entropy increases as the ordered ice becomes disordered liquid water)
Example 2
A hot reservoir at 600 K loses 5,000 J of heat to a cold reservoir at 300 K. What is the total entropy change of the universe?
Entropy change of hot reservoir: ΔSh = −Q/Th = −5000/600 = −8.33 J/K
Entropy change of cold reservoir: ΔSc = +Q/Tc = +5000/300 = +16.67 J/K
Total: ΔStotal = −8.33 + 16.67
ΔStotal = +8.34 J/K (positive, as required by the second law)
When to Use It
Use the entropy change formula to analyze the thermodynamic direction and feasibility of processes.
- Determining whether a process is spontaneous (ΔSuniverse > 0)
- Calculating entropy changes during phase transitions
- Analyzing heat engine cycles and refrigeration
- Understanding irreversibility in real-world processes