Thermodynamics Calculator | ΔG, ΔH, ΔS, Hess's Law & Carnot
Compute Gibbs free energy ΔG = ΔH − TΔS for chemical reactions at any temperature. Determines spontaneity, finds the crossover temperature where ΔG = 0, applies Hess's law to combine up to three reactions, and calculates Carnot engine efficiency, heat pump COP, and refrigerator COP.
PRESETS
ΔG (kJ/mol)
-817.884
Spontaneous (ΔG < 0)
T* (crossover, K)
3677.7
Temperature where ΔG = 0
Spontaneity
Spontaneous
Spontaneous below T* = 3677.7 K
Step-by-step:
ΔG = ΔH − T × ΔS/1000
= -890.000 − 298.0 × -242.000/1000
= -890.000 − -72.1160
= -817.8840 kJ/mol
ΔG AT MULTIPLE TEMPERATURES
| T (K) | ΔG (kJ/mol) | Spontaneous? |
|---|---|---|
| 248 | -829.984 | Yes |
| 298 | -817.884 | Yes |
| 348 | -805.784 | Yes |
| 398 | -793.684 | Yes |
What Is the Thermodynamics Calculator | ΔG, ΔH, ΔS, Hess's Law & Carnot?
Compute Gibbs free energy to determine reaction spontaneity at any temperature. Apply Hess's Law to combine up to three reactions. Calculate Carnot engine efficiency, work output, heat rejected, and COP for heat pump and refrigerator cycles.
Formula
ΔG = ΔH − T × ΔS/1000 (kJ/mol); T* = ΔH×1000/ΔS; η_Carnot = 1 − Tc/Th
How to Use
- 1
Choose the tab for your calculation: Gibbs Free Energy, Hess's Law, or Carnot Engine.
- 2
For Gibbs: enter ΔH (kJ/mol), ΔS (J/mol·K), and temperature T (K), or click a preset reaction.
- 3
Read ΔG (kJ/mol), spontaneity verdict, and crossover temperature T* where ΔG = 0.
- 4
Check the multi-temperature table to see how ΔG changes at T−50, T, T+50, T+100 K.
- 5
For Hess's Law: enter ΔH for each reaction, optionally reverse or scale it, and read the net ΔH.
- 6
For Carnot: enter hot reservoir Th, cold reservoir Tc, and heat input Qh to get efficiency, work, Qc, and COP.
- 7
All inputs are saved automatically so you can return to your calculation without re-entering values.
Select the Gibbs Free Energy, Hess's Law, or Carnot Engine tab for your calculation.
Example Calculation
Combustion of methane: ΔH = −890 kJ/mol, ΔS = −242 J/mol·K at T = 298 K → ΔG = −890 − (298 × −242/1000) = −890 + 72.1 = −817.9 kJ/mol. Highly spontaneous. T* = (−890 × 1000)/(−242) = 3678 K — reaction is spontaneous below that temperature.
Understanding Thermodynamics | ΔG, ΔH, ΔS, Hess's Law & Carnot
Spontaneity Classification
The signs of ΔH and ΔS together determine whether a reaction can ever be spontaneous and whether temperature drives the transition.
| ΔH | ΔS | Spontaneity | Example |
|---|---|---|---|
| − | + | Always spontaneous at all T | Combustion of H₂ |
| + | − | Never spontaneous (reverse is) | Reverse combustion |
| − | − | Spontaneous below T* = ΔH/ΔS × 1000 | Condensation of steam |
| + | + | Spontaneous above T* = ΔH/ΔS × 1000 | Melting of ice, NH₃ decomposition |
Standard Enthalpies of Formation (ΔH°f) at 298 K
These values (in kJ/mol) can be used with Hess's Law to compute ΔH° for any reaction: ΔH°rxn = Σ ΔH°f (products) − Σ ΔH°f (reactants).
| Compound | Formula | ΔH°f (kJ/mol) | Notes |
|---|---|---|---|
| Carbon dioxide | CO₂(g) | −393.5 | Most stable C oxide |
| Water (liquid) | H₂O(l) | −285.8 | Liquid; gas = −241.8 |
| Methane | CH₄(g) | −74.8 | Natural gas |
| Ammonia | NH₃(g) | −46.1 | Haber–Bosch product |
| Hydrogen chloride | HCl(g) | −92.3 | Strong acid gas |
| Sulfuric acid | H₂SO₄(l) | −814.0 | Concentrated liquid |
| Ethanol | C₂H₅OH(l) | −277.7 | Liquid fuel |
| Glucose | C₆H₁₂O₆(s) | −1274 | Biological fuel |
| Carbon monoxide | CO(g) | −110.5 | Incomplete combustion |
| Nitrogen dioxide | NO₂(g) | +33.2 | Endothermic formation |
Applications of Thermodynamic Calculations
- ›Industrial process design: identify which reactions are thermodynamically feasible at operating temperature.
- ›Haber–Bosch process for ammonia: ΔH < 0, ΔS < 0 — reaction is spontaneous below T*; engineers use moderate T (400–500 °C) as a compromise between yield and rate.
- ›Battery and fuel cell design: cell voltage relates directly to ΔG via ΔG = −nFE.
- ›Refrigeration and heat pumps: Carnot COP sets the theoretical maximum for energy efficiency.
- ›Biochemistry: ATP hydrolysis (ΔG° ≈ −30.5 kJ/mol) drives non-spontaneous metabolic reactions.
- ›Metallurgy: Ellingham diagrams plot ΔG° vs T to determine reduction feasibility of metal oxides.
- ›Environmental chemistry: spontaneity analysis helps predict whether pollutant reactions occur naturally.
Frequently Asked Questions
What does a negative ΔG mean?
ΔG < 0 means the reaction is spontaneous under the given conditions — it will proceed without continuous external energy input. ΔG > 0 is non-spontaneous and requires driving energy. ΔG = 0 means the system is at equilibrium.
What is the crossover temperature T*?
T* is the temperature where ΔG = 0. Below T* the reaction is spontaneous when ΔH and ΔS are both negative; above T* when both are positive. It equals ΔH×1000/ΔS (converting kJ to J). At T*, the system is at equilibrium.
What is Hess's Law and why is it useful?
Hess's Law states that the total enthalpy change for a reaction is independent of the route taken. This lets you add or reverse known reactions to derive ΔH for reactions that are hard to measure directly, such as the formation of CO₂ via CO intermediate.
What is the Carnot efficiency and why is it important?
The Carnot efficiency η = 1 − Tc/Th is the maximum possible efficiency for any heat engine operating between temperatures Tc and Th. No real engine can exceed it. It shows that efficiency improves by raising Th or lowering Tc.
How does ΔG relate to equilibrium constant K?
At standard conditions: ΔG° = −RT ln(K). If ΔG° is large and negative, K >> 1 and products are favored. If ΔG° is large and positive, K << 1 and reactants are favored. This calculator computes ΔG at any T; use ΔG° = −RT ln K for equilibrium calculations.
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