Entropy Change Calculator
Enter moles, heat capacity, temperatures and volume ratio to compute the entropy change of an ideal gas ΔS = n·Cv·ln(T2/T1) + n·R·ln(V2/V1).
Input Data
Results
At a glance:Entropy S is a measure of microscopic disorder; for a reversible process the entropy change of an ideal gas is ΔS = n·Cv·ln(T2/T1) + n·R·ln(V2/V1). The first term is the heat-driven change from temperature; the second is the expansion/compression contribution. Using Cp = Cv + R, the volume term can be written with pressure: ΔS = n·Cp·ln(T2/T1) − n·R·ln(P2/P1). Entropy is a state function, so ΔS depends only on initial and final states, not the path (so always evaluate along a reversible path). The second law requires total entropy of an isolated system to never decrease.
Formula
ΔS = n·Cv·ln(T2/T1) + n·R·ln(V2/V1)
Alternative: ΔS = n·Cp·ln(T2/T1) − n·R·ln(P2/P1)
R = 8.314 J/(mol·K)
$$\Delta S = n C_v \ln\frac{T_2}{T_1} + n R \ln\frac{V_2}{V_1}, \quad \Delta S_T = n C_v \ln\frac{T_2}{T_1}, \quad \Delta S_V = n R \ln\frac{V_2}{V_1}$$How to Use
- Enter moles n and Cv (J/mol·K).
- Enter initial and final temperatures (K) and the volume ratio V2/V1.
- The calculator returns ΔS and its temperature/volume terms.
Case Studies
Isothermal expansion
n = 1 mol, T constant, V2/V1 = 2.
ΔS = 0 + 1×8.314×ln2 ≈ 5.76 J/K.
Reversible expansion increases entropy by R·ln2 per mole.
FAQ
Is entropy a state function?
Yes. ΔS depends only on the initial and final equilibrium states. To compute it for any process, imagine a reversible path between the same states and integrate dQ_rev/T.
What does positive ΔS mean?
The system became more disordered (e.g. expanded or heated). For an isolated system, ΔS_total ≥ 0 is the second law.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.