# Entropy Change Calculator

Calculate entropy change for phase changes, temperature changes, and ideal mixing. Free thermodynamics calculator with spontaneity assessment.

## What this calculates

Calculate the entropy change (ΔS) for three common processes: phase changes (ΔS = q/T), temperature changes (ΔS = nCp·ln(T₂/T₁)), and ideal mixing (ΔS = -nRΣ(χi·lnχi)). Includes spontaneity assessment.

## Inputs

- **Calculation Type** — options: Phase Change (ΔS = q/T), Temperature Change (ΔS = nCp·ln(T₂/T₁)), Ideal Mixing (ΔS = -nRΣ(χi·lnχi)) — Select the type of entropy calculation.
- **Heat (q)** (J) — Heat absorbed during phase change in joules. Positive for endothermic (melting, vaporization).
- **Temperature** (K) — min 0.01 — Temperature of the phase change, or initial temperature T₁.
- **Final Temperature T₂** (K) — min 0.01 — Final temperature for temperature change calculation.
- **Moles (n)** (mol) — min 0 — Moles of substance.
- **Cp (Heat Capacity)** (J/(mol·K)) — min 0 — Molar heat capacity at constant pressure in J/(mol·K). Water: 75.3.
- **Mole Fraction χ1** — min 0.001, max 0.999 — Mole fraction of component 1 for mixing calculation.
- **Mole Fraction χ2** — min 0.001, max 0.999 — Mole fraction of component 2 for mixing calculation (should equal 1 - χ1 for a binary mixture).

## Outputs

- **ΔS** (J/K) — Entropy change in joules per kelvin.
- **ΔS per mole** (J/(mol·K)) — Entropy change per mole.
- **Spontaneity Assessment** — formatted as text — Interpretation of the entropy change.

## Details

Entropy (S) is a thermodynamic property that measures the degree of disorder or randomness in a system. The second law of thermodynamics states that the total entropy of an isolated system always increases in a spontaneous process.

Phase Change: ΔS = q_rev/T. For a reversible phase change at constant temperature and pressure, the entropy change equals the heat absorbed divided by the temperature. Vaporization has a large positive ΔS (increased disorder going from liquid to gas). Trouton's rule: ΔS_vap ≈ 85 J/(mol·K) for many liquids.

Temperature Change: ΔS = nCp·ln(T₂/T₁). When a substance is heated or cooled without phase change, the entropy change depends on the heat capacity and the ratio of final to initial temperature. Heating always increases entropy; cooling decreases it.

Ideal Mixing: ΔS_mix = -nRΣ(χi·lnχi). Mixing ideal gases or ideal solutions always increases entropy because the disorder increases when distinguishable particles are combined. This is always positive because χi < 1 and ln(χi) < 0.

## Frequently Asked Questions

**Q: What are the units of entropy?**

A: Entropy has units of energy per temperature: J/K (joules per kelvin) for total entropy, or J/(mol·K) for molar entropy. The SI unit is formally J/K. Some older references use cal/(mol·K) or entropy units (eu).

**Q: Is a positive or negative ΔS favorable?**

A: A positive ΔS (increasing entropy) favors spontaneity. However, spontaneity also depends on enthalpy: ΔG = ΔH - TΔS. A process can be spontaneous even with negative ΔS if ΔH is sufficiently negative (exothermic). Temperature determines the relative importance of each factor.

**Q: What is Trouton's rule?**

A: Trouton's rule states that the entropy of vaporization (ΔS_vap) is approximately 85 J/(mol·K) for many liquids at their normal boiling point. This corresponds to ΔH_vap/T_bp. Exceptions include water (109 J/(mol·K), due to hydrogen bonding) and low-boiling gases.

**Q: Why does mixing always increase entropy?**

A: Mixing increases the number of possible arrangements (microstates) of the molecules. Before mixing, each component occupies its own container. After mixing, each molecule has access to the entire combined volume. This increased number of arrangements corresponds to greater entropy.

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Source: https://vastcalc.com/calculators/chemistry/entropy
Category: Chemistry
Last updated: 2026-04-21