16.7785
J/(mol·K)
0.016779
kJ/(mol·K)
5,000
J/mol
16.7785
J/(mol·K)
100
J/(mol·K)
16.7785
J/(mol·K)
0.016779
kJ/(mol·K)
5,000
J/mol
16.7785
J/(mol·K)
100
J/(mol·K)
The Entropy Calculator computes the entropy change (ΔS) for chemical and physical processes using two methods: the Clausius definition (ΔS = qrev/T) and the standard entropy method (ΔS° = ΣS°(products) − ΣS°(reactants)). Entropy is the thermodynamic measure of disorder or the number of microstates available to a system. According to the second law of thermodynamics, the total entropy of an isolated system always increases in a spontaneous process. This calculator also computes TΔS, the entropy contribution to Gibbs free energy, essential for determining spontaneity at any temperature.
Method 1 — Clausius Definition:
$$\Delta S = \frac{q_{rev}}{T}$$
where qrev is the heat transferred reversibly (in J) and T is the absolute temperature (in K). This applies to isothermal processes like phase changes.
Method 2 — Standard Entropies:
$$\Delta S^\circ_{rxn} = \sum S^\circ(\text{products}) - \sum S^\circ(\text{reactants})$$
Standard molar entropies (S°) are tabulated values at 298 K and 1 atm. Unlike ΔH°f, S° values for elements are not zero — they reflect the absolute entropy from the third law of thermodynamics.
The TΔS term appears in the Gibbs free energy equation:
$$\Delta G = \Delta H - T\Delta S$$
Positive ΔS means the system becomes more disordered (entropy increases) — favored by nature. Negative ΔS means increased order. Reactions that produce more gas molecules, dissolve solids, or increase temperature generally have positive ΔS. The TΔS value tells you the entropy contribution to spontaneity: a large positive TΔS favors spontaneous reaction (makes ΔG more negative).
Inputs
Results
ΔS = 6010 J / 273 K = 22.01 J/(mol·K). The heat of fusion of ice is 6.01 kJ/mol. Positive ΔS reflects the increase in disorder from solid to liquid.
Inputs
Results
ΣS°(products) = 2(69.9) = 139.8 J/(mol·K). ΣS°(reactants) = 2(130.7) + 205.2 − 74.9 ≈ 391.7. ΔS° = 139.8 − 391.7 = −251.9 J/(mol·K). Negative because 3 moles of gas → 2 moles of liquid.
Entropy (S) is a thermodynamic property that measures the degree of randomness or disorder in a system. It is related to the number of microstates (W) by Boltzmann's equation: S = kB ln W.
The second law states that the total entropy of an isolated system can only increase or remain the same. For any spontaneous process, ΔSuniverse = ΔSsystem + ΔSsurroundings > 0.
The third law states that the entropy of a perfect crystal at absolute zero (0 K) is exactly zero. This provides a reference point for measuring absolute entropies.
Unlike enthalpies of formation, standard entropies (S°) are absolute values based on the third law. Even elements have disorder at 298 K, so S° > 0 for all substances above 0 K.
Processes that increase entropy include: melting, vaporization, dissolution, reactions producing more gas molecules, heating, and expansion. Essentially, any process that increases disorder.
Yes, the entropy of a system can decrease (e.g., freezing water). However, the surroundings' entropy must increase by at least as much, ensuring the total universe entropy increases.
Through the Gibbs free energy equation: ΔG = ΔH − TΔS. A positive TΔS term (increasing entropy) favors spontaneity. At high temperatures, the TΔS term dominates.
Entropy has units of J/(mol·K) or J/K. The SI unit is joules per kelvin. Older literature may use cal/(mol·K) or entropy units (e.u.).
When two ideal gases mix at constant T and P, ΔSmix = −nR(x₁ ln x₁ + x₂ ln x₂), which is always positive. Mixing always increases entropy.
Entropy is measured by integrating Cp/T from 0 K to the desired temperature: S° = ∫(Cp/T)dT + contributions from phase transitions. Calorimetric measurements of heat capacity provide the data.
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