About the Entropy Change Calculator
This entropy change calculator works out ΔS, the change in entropy of a system, for the processes met in introductory thermodynamics: heating or cooling a substance (ΔS = mc ln(T₂/T₁)), a phase change at constant temperature such as melting ice or boiling water (ΔS = mL/T), the expansion or compression of an ideal gas with any change in temperature and volume, and a simple reversible heat transfer at constant temperature (ΔS = Q/T).
It is built for chemistry and physics students checking homework, engineering students reviewing the second law, and teachers preparing examples. Results are in joules per kelvin, along with the heat involved where it is well defined, and the heating mode charts how entropy builds up as the temperature rises — quickly at first, then more slowly, because each joule matters less at higher temperature.
All formulas assume reversible paths and constant specific heat or latent heat, which is accurate over moderate temperature ranges. Because entropy is a state function, the same ΔS applies to any real process between the same start and end states. Temperatures can be entered in °C, °F or K, but they are always converted to kelvin, since entropy calculations need absolute temperature.
With the default inputs, the entropy change δs is 779.4687 J/K. Change any value above to recalculate instantly.
How to use the entropy change calculator
- 1Choose the process: heating, phase change, ideal gas, or heat at constant temperature.
- 2Enter the mass and specific or latent heat, or the moles and volumes of gas.
- 3Enter the temperatures and pick °C, °F or K.
- 4For freezing or condensing, switch on “heat released”.
- 5Read ΔS in J/K; a positive value means entropy increased.
Formula and method
Entropy change is defined for a reversible path as ΔS = ∫ dQ/T. When a substance with constant specific heat is heated, dQ = mc dT, and integrating gives ΔS = mc ln(T₂/T₁). During a phase change the temperature stays fixed, so the whole latent heat is divided by that one absolute temperature; the sign is negative when heat is released, as in freezing or condensing.
For an ideal gas, entropy depends on both temperature and volume: ΔS = nCv ln(T₂/T₁) + nR ln(V₂/V₁), with R = 8.314462618 J/(mol·K). Cv is taken as 3/2 R for monatomic gases, 5/2 R for diatomic gases near room temperature and about 3R for simple polyatomic gases. At constant temperature only the volume term remains. Because entropy is a state function, these results hold for any process — reversible or not — that connects the same two states.
- ΔS
- Entropy change (J/K)
- m
- Mass (kg)
- c
- Specific heat capacity (J/(kg·K))
- L
- Latent heat of fusion or vaporisation (J/kg)
- T, T₁, T₂
- Absolute temperatures (K)
- n
- Amount of gas (mol)
- Cv
- Molar heat capacity at constant volume (J/(mol·K))
- R
- Molar gas constant, 8.314462618 J/(mol·K)
- V₁, V₂
- Initial and final volume (any consistent unit)
- Q
- Heat added reversibly (J)
Worked examples
Heating 1 kg of water from 20 °C to 80 °C
ΔS = 1 × 4,186 × ln(353.15 / 293.15) = 4,186 × 0.18621 = 779.5 J/K. The heat absorbed is 1 × 4,186 × 60 = 251,160 J.
Melting 1 kg of ice at 0 °C
The latent heat of fusion is 334,000 J, all absorbed at 273.15 K, so ΔS = 334,000 / 273.15 = 1,222.8 J/K.
1 mol of gas doubling its volume at constant temperature
With no temperature change only the volume term remains: ΔS = 1 × 8.3145 × ln 2 = 5.763 J/K.
Heating 2 mol of nitrogen from 300 K to 600 K at constant volume
For a diatomic gas Cv = 5/2 R = 20.786 J/(mol·K), so ΔS = 2 × 20.786 × ln 2 = 28.82 J/K.
1,000 J of heat added at 300 K
At constant temperature ΔS = Q/T = 1,000 / 300 = 3.33 J/K.
Frequently asked questions
What is the formula for entropy change?+
The general definition is ΔS = ∫ dQ_rev / T. It reduces to ΔS = Q/T at constant temperature, ΔS = mc ln(T₂/T₁) for heating with constant specific heat, and ΔS = mL/T for a phase change.
What are the units of entropy?+
Entropy is measured in joules per kelvin (J/K). Specific entropy is J/(kg·K) and molar entropy is J/(mol·K). Chemistry tables often list standard molar entropies in J/(mol·K).
Why must temperature be in kelvin?+
Entropy divides heat by absolute temperature, so the zero point matters. Using °C would make ΔS infinite at 0 °C and give the wrong sign below it. The calculator converts every temperature to kelvin.
Can entropy decrease?+
Yes, the entropy of a system can decrease, for example when water freezes or a gas is compressed and cooled. The second law only requires the total entropy of the system plus its surroundings to stay the same or increase.
What is the entropy change when water boils?+
Boiling 1 kg of water at 100 °C absorbs 2,257 kJ, so ΔS = 2,257,000 / 373.15 ≈ 6,049 J/K — about five times the entropy gained by melting the same mass of ice.
Does free expansion of a gas change entropy?+
Yes. Even though no heat flows in a free expansion, entropy is a state function, so ΔS = nR ln(V₂/V₁) — the same as the reversible isothermal expansion between the same states. For 1 mol doubling in volume that is 5.76 J/K.