Entropy Calculator
Find the entropy change delta S when a substance is heated or cooled at constant pressure, from moles, molar heat capacity, and start and end temperature.
🌀 What is Entropy Change?
Entropy change (written ΔS) measures how much a substance's entropy, a thermodynamic quantity often described as a measure of disorder or of the number of ways energy can be distributed, increases or decreases when it is heated or cooled. This calculator finds the classical, macroscopic entropy change of heating or cooling a fixed amount of substance at constant pressure, using its molar heat capacity and the starting and ending temperatures.
This calculation is a standard building block across general chemistry and thermodynamics courses: computing the entropy change step of a Carnot cycle or other thermodynamic cycle, evaluating the entropy term in Gibbs free energy calculations to judge whether heating a reaction mixture helps or hurts spontaneity, comparing how "sensitive" different substances are to temperature change based on their heat capacity, and building toward more complete entropy calculations that also include phase changes and pressure or volume changes.
A common point of confusion is assuming a bigger temperature change always means a bigger entropy change in direct proportion. It does not, because the formula uses a natural logarithm of the temperature ratio, not the temperature difference itself. Doubling the absolute temperature produces a much smaller entropy change than doubling the heat capacity does, since the logarithm compresses large ratios into comparatively small numbers.
This calculator is useful because it applies the correct logarithmic relationship automatically and reports the answer in both total (J/K, scaled to your actual sample size) and molar (J/mol·K, per-mole) form, letting you use whichever version a given problem calls for without redoing the arithmetic by hand.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Heating Nitrogen Gas
n = 2 mol, Cp = 29.1 J/(mol·K), T₁ = 298 K, T₂ = 373 K.
Example 2 — Cooling Liquid Water
n = 1 mol, Cp = 75.3 J/(mol·K), T₁ = 350 K, T₂ = 250 K.
Example 3 — Doubling the Temperature
n = 0.5 mol, Cp = 20.8 J/(mol·K), T₁ = 300 K, T₂ = 600 K.
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for entropy change when heating a substance?
At constant pressure with no phase change, entropy change is delta S = n times Cp times the natural log of T2 divided by T1, where n is moles, Cp is molar heat capacity at constant pressure in J/(mol K), and T1 and T2 are the initial and final temperatures in Kelvin.
Why is entropy change negative when a substance cools down?
When T2 is less than T1, the ratio T2 divided by T1 is less than 1, and the natural logarithm of a number less than 1 is negative. This matches physical intuition, cooling a substance removes thermal energy and reduces the number of ways that energy can be distributed among its particles, so entropy decreases.
What units should I use for heat capacity in this calculator?
Enter molar heat capacity at constant pressure, Cp, in joules per mole per Kelvin, J/(mol K). If you only have specific heat capacity in J/(g K), multiply it by the substance's molar mass in g/mol first to convert it to molar heat capacity.
Why do I need temperature in Kelvin, not Celsius?
The formula uses a ratio of temperatures, T2 divided by T1, inside a logarithm, and that ratio is only physically meaningful on an absolute temperature scale where zero means true zero thermal energy. Celsius has an arbitrary zero point, so a Celsius-based ratio would give a nonsensical result.
Does this calculator account for phase changes like melting or boiling?
No. This formula assumes the substance stays in a single phase (all liquid, or all gas, for example) across the entire temperature range, with a constant heat capacity. A phase change happening between T1 and T2 needs to be handled with a separate ΔS = ΔH divided by T calculation at the transition temperature, then added to the heating term for each individual phase.
How is entropy change related to spontaneity of a reaction?
Entropy change of the system alone does not determine spontaneity, only entropy change of the entire universe, system plus surroundings, does, via the second law of thermodynamics. In practice, chemists usually combine entropy with enthalpy through Gibbs free energy, delta G = delta H minus T delta S, to judge whether a process is spontaneous at a given temperature.
What is the difference between total entropy change and molar entropy change?
Total entropy change, in J/K, is the entropy change for the entire sample you actually have, scaled by the number of moles present. Molar entropy change, in J/(mol K), is the entropy change per single mole, independent of sample size, useful for comparing substances directly regardless of how much of each you have.
Is this the same kind of entropy as statistical mechanics entropy?
No, though they describe the same underlying physical quantity from a different angle. This calculator uses the classical, macroscopic thermodynamic definition based on heat capacity and reversible heat transfer. Statistical mechanics instead computes entropy directly from counting microscopic arrangements, S = kB ln(W), which this site's Boltzmann Entropy Calculator and Gibbs Entropy Calculator handle separately.
Can entropy change ever be exactly zero?
Yes, whenever T2 equals T1, meaning no net temperature change occurred, the ratio T2/T1 equals 1, and the natural log of 1 is exactly 0, so delta S is 0 regardless of the substance's heat capacity or the number of moles present.
Why does a substance with a higher heat capacity show a bigger entropy change for the same temperature change?
Heat capacity measures how much heat is needed to raise temperature by one degree. A substance with a higher Cp absorbs (or releases) more heat for the same temperature change, and since entropy change is directly proportional to Cp in this formula, that extra heat transfer produces a proportionally larger entropy change.