Entropy Change Calculator (Thermodynamics)
Calculate entropy change (ΔS) for chemical and physical processes using the fundamental thermodynamic relationship.
Find entropy from heat transfer, temperature, and reactions.
What Is Entropy?
Entropy (S) is a thermodynamic state function that quantifies the disorder or randomness of a system — more precisely, the number of microscopic arrangements (microstates) available to a system. The greater the number of possible microstates, the higher the entropy.
Ludwig Boltzmann gave entropy its microscopic definition in 1877: S = k × ln(W) where k is Boltzmann’s constant (1.381 × 10⁻²³ J/K) and W is the number of microstates. This equation is inscribed on Boltzmann’s tombstone in Vienna.
The Second Law of Thermodynamics
The Second Law states that in any spontaneous process, the total entropy of the universe increases — or at minimum stays the same. In other words: ΔS_universe ≥ 0. Spontaneous processes naturally move toward higher entropy states.
Common examples of entropy increase:
- Ice melting into water (ordered crystal → disordered liquid)
- A drop of dye diffusing through water
- Gas expanding to fill a larger container
- Scrambling an egg (cannot unscramble it spontaneously)
Key Formulas
Heat transfer: ΔS = q_rev / T (in Kelvin). For a reversible heat transfer, entropy change equals the heat transferred divided by the absolute temperature.
Gibbs-Helmholtz equation: ΔG = ΔH - TΔS where:
- ΔG = Gibbs free energy change (J/mol or kJ/mol)
- ΔH = Enthalpy change (J/mol or kJ/mol)
- T = Temperature (Kelvin)
- ΔS = Entropy change (J/mol·K)
Spontaneity Conditions (Gibbs Free Energy)
| ΔH | ΔS | ΔG | Spontaneous? |
|---|---|---|---|
| Negative | Positive | Always negative | Always spontaneous |
| Negative | Negative | Depends on T | Spontaneous at low T |
| Positive | Positive | Depends on T | Spontaneous at high T |
| Positive | Negative | Always positive | Never spontaneous |
When ΔH and ΔS have the same sign, there is a crossover temperature where ΔG = 0: T_crossover = ΔH / ΔS. Above this temperature (for positive ΔH and ΔS), the reaction becomes spontaneous.
Ice Melting Example
At 0°C (273.15 K), ice melts reversibly. ΔH_fusion of water = +6,010 J/mol (endothermic — requires heat input). ΔS = ΔH / T = 6,010 / 273.15 = 22.0 J/mol·K. The positive entropy change reflects increased disorder as the rigid ice crystal becomes liquid water.
Gibbs Free Energy and Equilibrium
When ΔG = 0, the reaction is at equilibrium — forward and reverse rates are equal. When ΔG < 0, the forward reaction is spontaneous (products are favored). When ΔG > 0, the reverse reaction is spontaneous (reactants are favored). This is fundamental to predicting whether a chemical reaction will proceed under given conditions.
Standard Entropy Values
Standard entropy (S°) values are tabulated at 298 K and 1 atm. To find ΔS° for a reaction: ΔS°_rxn = Σ S°(products) - Σ S°(reactants). These values are available in thermodynamics tables in any chemistry textbook.