Skip to main content

All Calculators & Converters

All calculators

Entropy Calculator

Compute entropy changes ΔS for common thermodynamic processes: isothermal ideal-gas expansion/compression, heating/cooling with constant heat capacity, phase changes, and ideal-gas mixing. Shows steps and an optional ΔS mini chart (system, surroundings, total).

Background

Entropy change is defined by the reversible path heat divided by temperature, dS = δq_rev/T. For typical course problems we use standard models: ideal gases, constant heat capacities, and tabulated enthalpies for phase changes. When possible, we also estimate surroundings’ entropy to illustrate the second law via ΔS_total = ΔS_sys + ΔS_surr.

Choose a mode and enter values

Mode:

Isothermal ideal gas (ΔS = nR ln(V₂/V₁) = nR ln(P₁/P₂))

Heating/Cooling at constant heat capacity (ΔS = C ln(T₂/T₁))

Phase change at constant T (ΔS = ΔH_trans/T)

Ideal-gas mixing (two components)

Options:

Step-by-step working

Mini chart: ΔS_sys, ΔS_surr, ΔS_total

Round to sensible significant figures

Surroundings (optional):

If provided, we estimate ΔS_surr ≈ −q_sys/T_surr and report ΔS_total.

Given:

ΔS = nR ln(V₂/V₁) = nR ln(P₁/P₂). Use ratio > 0.

Quick picks:

Chips prefill fields; you can edit and recalculate.

Result:

No results yet. Choose a mode and enter values.

How to use this calculator

Isothermal: enter moles and a valid ratio (V₂/V₁ or P₁/P₂).
Heating/Cooling: pick Cp/Cv/Custom C, set basis (per mol/gram/total), provide T₁, T₂, and amount if needed.
Phase change: enter n, ΔH_trans (kJ·mol⁻¹), and T (K).
Mixing: give n₁ and n₂ (ideal gases). We compute xᵢ and ΔS_mix.
Surroundings (optional): set T_surr to estimate ΔS_surr and ΔS_total.

Units: T in K; R = 8.314462618 J·mol⁻¹·K⁻¹; natural logarithms.

Formula & Equation Used

Isothermal ideal gas:

ΔS = n R ln (\frac{V_{2}}{V_{1}}) = n R ln (\frac{P_{1}}{P_{2}}), T constant

Heating/Cooling (constant heat capacity):

ΔS = C ln (\frac{T_{2}}{T_{1}}), C = nCₚ, nCᵥ, mc, or total

Phase change at constant T:

ΔS = n {ΔH}_{trans} / T

Ideal-gas mixing (two components):

{ΔS}_{mix} = - R \sum n_{i} ln x_{i}, xᵢ = nᵢ / (n₁ + n₂)

Surroundings and total:

{ΔS}_{surr} \approx - q_{sys} / T_{surr}, ΔS = {ΔS}_{sys} + {ΔS}_{surr}

Example Problems & Step-by-Step Solutions

Example 1 — Isothermal expansion

n=1.00 mol ideal gas expands isothermally with V₂/V₁=2.00.
ΔS = nR ln(2.00) = 1.00×8.314×0.693 = 5.76 J·K⁻¹. (q>0 to system; if T_surr=T, ΔS_total=0.)

Example 2 — Heating at constant Cp

Cp=75.3 J·mol⁻¹·K⁻¹, n=1.00 mol, T: 298→350 K.
C = n·Cp = 75.3 J·K⁻¹; ΔS = 75.3 ln(350/298) = 11.7 J·K⁻¹.

Example 3 — Vaporization

n=0.500 mol, ΔH_vap=40.65 kJ·mol⁻¹, T=373.15 K.
ΔS = n·ΔH/T = 0.500×40650/373.15 = 54.5 J·K⁻¹.

Frequently Asked Questions

Q: Should I use natural or base-10 logs?

Use natural logarithms (ln). The gas constant is in J·mol⁻¹·K⁻¹.

Q: Can I enter temperatures in °C?

Please convert to Kelvin: T(K)=T(°C)+273.15.

Q: How do I get ΔS_total?

Provide an ambient T_surr. We estimate ΔS_surr≈−q_sys/T_surr for the modeled reversible path.

1. Intro to General Chemistry

19. Chemical Thermodynamics

Entropy Calculations - Part 1 of 2

19. Chemical Thermodynamics

Entropy Calculations - Part 2 of 2

19. Chemical Thermodynamics

Entropy Calculations: Phase Changes

19. Chemical Thermodynamics

Third Law of Thermodynamics

19. Chemical Thermodynamics

Gibbs Free Energy

19. Chemical Thermodynamics

Gibbs Free Energy & Equilibrium

19. Chemical Thermodynamics

Cell Potential and Gibbs Free Energy

20. Electrochemistry

Standard Temperature and Pressure

8. Thermochemistry

First Law of Thermodynamics -

8. Thermochemistry

Enthalpy of Formation

8. Thermochemistry

1. Intro to General Chemistry - Part 1 of 3

7 topics 12 problems

1. Intro to General Chemistry - Part 2 of 3

5 topics 11 problems

1. Intro to General Chemistry - Part 3 of 3

5 topics 11 problems

19. Chemical Thermodynamics - Part 1 of 2

5 topics 11 problems

19. Chemical Thermodynamics - Part 2 of 2

3 topics 10 problems

20. Electrochemistry - Part 1 of 3

4 topics 11 problems

20. Electrochemistry - Part 2 of 3

4 topics 11 problems

20. Electrochemistry - Part 3 of 3

5 topics 11 problems

7. Gases - Part 1 of 4

5 topics 14 problems

7. Gases - Part 2 of 4

5 topics 13 problems

7. Gases - Part 3 of 4

5 topics 13 problems

7. Gases - Part 4 of 4

5 topics 13 problems

8. Thermochemistry - Part 1 of 3

5 topics 13 problems

8. Thermochemistry - Part 2 of 3

5 topics 13 problems

8. Thermochemistry - Part 3 of 3

5 topics 13 problems

Gibbs Free Energy

6. Thermodynamics and Kinetics

6. Thermodynamics and Kinetics

6. Thermodynamics and Kinetics

6. Thermodynamics and Kinetics - Part 1 of 2

4 topics 11 problems

6. Thermodynamics and Kinetics - Part 2 of 2

4 topics 10 problems

Angular Momentum & Newton's Second Law

16. Angular Momentum

20. Heat and Temperature

Linear Thermal Expansion

20. Heat and Temperature

Volume Thermal Expansion

20. Heat and Temperature

Specific Heat & Temperature Changes

20. Heat and Temperature

Latent Heat & Phase Changes

20. Heat and Temperature

Calorimetry with Temperature and Phase Changes

20. Heat and Temperature

Advanced Calorimetry: Equilibrium Temperature with Phase Changes

20. Heat and Temperature

20. Heat and Temperature

First Law of Thermodynamics

22. The First Law of Thermodynamics

Heat Engines and the Second Law of Thermodynamics

23. The Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

23. The Second Law of Thermodynamics

Statistical Interpretation of Entropy

23. The Second Law of Thermodynamics

16. Angular Momentum

7 topics 14 problems

20. Heat and Temperature - Part 1 of 2

5 topics 12 problems

20. Heat and Temperature - Part 2 of 2

4 topics 11 problems

22. The First Law of Thermodynamics

5 topics 13 problems

23. The Second Law of Thermodynamics - Part 1 of 2

4 topics 9 problems

23. The Second Law of Thermodynamics - Part 2 of 2

4 topics 8 problems

Laws of Thermodynamics

7. Energy and Metabolism

7. Energy and Metabolism

10 topics 13 problems

Laws of Thermodynamics

3. Energy & Cell Processes

3. Energy & Cell Processes - Part 1 of 4

10 topics 12 problems

3. Energy & Cell Processes - Part 2 of 4

10 topics 9 problems

3. Energy & Cell Processes - Part 3 of 4

8 topics 11 problems

3. Energy & Cell Processes - Part 4 of 4

7 topics 10 problems

Temperature (Simplified)

1. Matter and Measurements

First Law of Thermodynamics

7. Energy, Rate and Equilibrium

7. Energy, Rate and Equilibrium

Entropy (Simplified)

7. Energy, Rate and Equilibrium

Gibbs Free Energy (Simplified)

7. Energy, Rate and Equilibrium

Solubility: Temperature Effect

1. Matter and Measurements - Part 1 of 3

7 topics 15 problems

1. Matter and Measurements - Part 2 of 3

7 topics 15 problems

1. Matter and Measurements - Part 3 of 3

7 topics 15 problems

7. Energy, Rate and Equilibrium - Part 1 of 3

5 topics 11 problems

7. Energy, Rate and Equilibrium - Part 2 of 3

5 topics 11 problems

7. Energy, Rate and Equilibrium - Part 3 of 3

3 topics 8 problems

9. Solutions - Part 1 of 3

5 topics 12 problems

9. Solutions - Part 2 of 3

7 topics 11 problems

9. Solutions - Part 3 of 3

7 topics 11 problems

Standard Temperature and Pressure

Solubility: Temperature Effect

Temperature (Simplified)

3. Matter and Energy

First Law of Thermodynamics

3. Matter and Energy

3. Matter and Energy

10 topics 30 problems

13. Solutions - Part 1 of 2

12 topics 36 problems

13. Solutions - Part 2 of 2

2 topics 6 problems

3. Matter and Energy - Part 1 of 2

12 topics 36 problems

3. Matter and Energy - Part 2 of 2

1 topic 3 problems

Laws of Thermodynamics

12. Microbial Metabolism

12. Microbial Metabolism - Part 1 of 3

9 topics 14 problems

12. Microbial Metabolism - Part 2 of 3

6 topics 13 problems

12. Microbial Metabolism - Part 3 of 3

8 topics 13 problems

Gibbs Free Energy and Equilibrium

3. Energy - Part 1 of 2

4 topics 9 problems

3. Energy - Part 2 of 2

3 topics 8 problems

Chemical Thermodynamics: Entropy

6. Chemical Equilibrium

Chemical Thermodynamics: Enthalpy

6. Chemical Equilibrium

Chemical Thermodynamics: Gibbs Free Energy

6. Chemical Equilibrium

6. Chemical Equilibrium - Part 1 of 3

4 topics 12 problems

6. Chemical Equilibrium - Part 2 of 3

4 topics 12 problems

6. Chemical Equilibrium - Part 3 of 3

2 topics 6 problems

1. Introduction to Biochemistry

Second Law of Thermodynamics

1. Introduction to Biochemistry

Gibbs Free Energy

1. Introduction to Biochemistry

Thermodynamics of Membrane Diffusion: Charged Ion

11. Biological Membranes and Transport

Thermodynamics of Membrane Diffusion: Uncharged Molecule

11. Biological Membranes and Transport

Reversible Inhibition

7. Enzyme Inhibition and Regulation

Irreversible Inhibition

7. Enzyme Inhibition and Regulation

Recap of Reversible Inhibition

7. Enzyme Inhibition and Regulation

1. Introduction to Biochemistry - Part 1 of 4

5 topics 14 problems

1. Introduction to Biochemistry - Part 2 of 4

5 topics 13 problems

1. Introduction to Biochemistry - Part 3 of 4

5 topics 13 problems

1. Introduction to Biochemistry - Part 4 of 4

5 topics 13 problems

11. Biological Membranes and Transport - Part 1 of 4

5 topics 13 problems

11. Biological Membranes and Transport - Part 2 of 4

5 topics 12 problems

11. Biological Membranes and Transport - Part 3 of 4

5 topics 12 problems

11. Biological Membranes and Transport - Part 4 of 4

5 topics 12 problems

7. Enzyme Inhibition and Regulation - Part 1 of 5

5 topics 15 problems

7. Enzyme Inhibition and Regulation - Part 2 of 5

5 topics 14 problems

7. Enzyme Inhibition and Regulation - Part 3 of 5

6 topics 14 problems

7. Enzyme Inhibition and Regulation - Part 4 of 5

5 topics 14 problems

7. Enzyme Inhibition and Regulation - Part 5 of 5

5 topics 14 problems