Second Law Entropy⚠ unverified
Physics / Thermodynamics · Compute the entropy change for a reversible process
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Q | Q | J | 1.0 | Heat transferred |
| T | T | K | 1.0 | Absolute temperature |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | ΔS | J/K | Entropy change, in joules per kelvin (J/K). Returns positive infinity if ``T`` is not positive |
The science & history
Understanding the Parameters
- $Q$ — heat into the system positive if you want $\Delta S > 0$ for heating.
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$T$ — absolute temperature of the boundary / reservoir. Never use degC in the denominator without converting to K.
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$\Delta S$ — for an isothermal reversible process in an ideal system, this is the full entropy change; otherwise it is only the heat-transfer contribution, not $S_{\mathrm{gen}}$.
Derivation (Approaching a Proof)
Clausius defined $dS = \delta Q_{\mathrm{rev}}/T$. Integrating at constant $T$:
$$\Delta S = \frac{Q_{\mathrm{rev}}}{T}.$$
The second law states $\oint \delta Q/T \le 0$ for a cycle (equality when reversible), equivalent to $S_{\mathrm{gen}} \ge 0$ for any process. Related: Entropy Change Ideal Gas for state-to-state $\Delta S$ without assuming isothermal heat, and Exergy Destruction $T_0 S_{\mathrm{gen}}$.
History
Rudolf Clausius introduced entropy (1865) to express the second law quantitatively; $dS = \delta Q/T$ is the starting definition in classical thermodynamics.
Related Concepts: Entropy Change Ideal Gas, Exergy Destruction, Carnot Efficiency, First Law DeltaU
Notes: Registry calculator second-law-entropy (unverified). Isothermal / $Q/T$ form only — not a
full entropy balance with generation.