Entropy Change Calculator (ΔS)
Calculate the entropy change ΔS for three standard thermodynamic scenarios: reversible isothermal heat transfer (ΔS = Q/T), heating or cooling a substance (ΔS = mcₚ ln T₂/T₁), or isothermal expansion of an ideal gas (ΔS = nR ln V₂/V₁).
Calculation method
J
K
Entropy increases (more disorder / more microstates)
Heat transferred Q
Absolute temperature T
ΔS = Q / T
How does this calculator work?
Three formulas cover most introductory entropy calculations: ΔS = Q/T (isothermal heat transfer), ΔS = mcₚ ln(T₂/T₁) (heating/cooling a substance; temperatures in Kelvin), and ΔS = nR ln(V₂/V₁) (ideal gas expansion; R = 8.314 J/mol·K). Positive ΔS = more disorder. The second law says total entropy of the universe never decreases.
Formula
How this is calculated
Entropy (S) measures the number of microscopic arrangements (microstates) accessible to a system — loosely, its degree of molecular disorder. The second law of thermodynamics states that the total entropy of an isolated system never decreases over time.
For a reversible isothermal process, entropy change equals the reversible heat flow divided by absolute temperature: ΔS = Q/T (Q in joules, T in Kelvin). When heat flows into the system (Q > 0), entropy increases; when it flows out, entropy decreases. This formula also applies to isothermal phase transitions such as melting or boiling at constant pressure. For heating or cooling a single-phase substance, integrating dS = dQ/T = m cₚ dT/T gives ΔS = m × cₚ × ln(T₂/T₁) — temperatures must be in Kelvin (no zeros or negatives). For the isothermal expansion of an ideal gas: ΔS = n × R × ln(V₂/V₁), where n is moles, R = 8.314 J/(mol·K); expansion (V₂ > V₁) always increases entropy because more spatial microstates become accessible.
All three formulas assume reversible, quasi-static processes at thermodynamic equilibrium. Real irreversible processes — free expansion, mixing, friction — generate additional positive entropy beyond these values. The entropy change of the surroundings (−Q/T_surroundings) must also be considered to find the total entropy produced by the universe.
Frequently asked questions
The formula ΔS = Q/T requires an absolute temperature scale. At 0 K, all classical thermal motion ceases and entropy reaches its minimum. Celsius and Fahrenheit are relative scales with arbitrary zeros — a negative Celsius temperature would give a nonsensical negative denominator. Convert: K = °C + 273.15.
Yes — a system's local entropy can decrease (e.g. water freezing into ice reduces liquid-phase entropy) provided the surroundings gain at least as much entropy. The second law requires only that the TOTAL entropy of the universe (system + surroundings) does not decrease, not every individual subsystem.
Gibbs free energy ΔG = ΔH − TΔS determines spontaneity at constant temperature and pressure: ΔG < 0 means the process is spontaneous. A positive entropy change (TΔS > 0) favours spontaneity; a negative one opposes it. Neither ΔS alone nor ΔH alone is decisive — both contribute to ΔG.
Also known as
TG we-Calculate Editorial Team. (2026). Entropy Change Calculator (ΔS) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/entropy-calculator
TG we-Calculate Editorial Team. "Entropy Change Calculator (ΔS)." TG we-Calculate. 2026. https://we-calculate.com/calculator/entropy-calculator.
TG we-Calculate Editorial Team, "Entropy Change Calculator (ΔS)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/entropy-calculator
@misc{wecalculate_entropy_calculator, title = {Entropy Change Calculator (ΔS)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/entropy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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