Model boiling and condensation with simple logarithmic scaling. Switch units, solve variable, and export results. Ideal for labs, design checks, and quick daily comparisons.
For many phase transitions where the vapor behaves ideally and the latent heat is approximately constant over the temperature interval, an integrated form is used:
ln(P2 / P1) = -(ΔH / R) · (1/T2 - 1/T1)
Tip: keep temperature spacing reasonable if estimating ΔH.
| Case | Solve for | P1 (kPa) | T1 (C) | T2 (C) | ΔH (kJ/mol) | Result |
|---|---|---|---|---|---|---|
| 1 | P2 | 101.325 | 100 | 120 | 40.7 | Higher P2 at higher temperature |
| 2 | T2 | 10 | 25 | — | 44.0 | Find temperature for target pressure |
| 3 | ΔH | 5 | 20 | 80 | — | Estimate latent heat from two points |
The integrated Clausius Clapeyron relation links equilibrium pressure and temperature during a phase change. With one known point (P1, T1) and an approximate latent heat, it predicts a second point (P2, T2). It supports fast estimates of vapor-pressure and boiling-point shifts.
The calculator applies ln(P2/P1) = -(ΔH/R)(1/T2 - 1/T1). Temperatures convert to kelvin to preserve the absolute scale. The gas constant R = 8.314462618 J/(mol·K) keeps ΔH consistent in J/mol or kJ/mol.
Use an equilibrium pressure and temperature pair for the same substance and phase transition. For example, water has ΔHvap of about 40.7 kJ/mol near 100 °C. If your data are far from the chosen range, uncertainty grows because ΔH changes with temperature.
This integrated form assumes latent heat stays roughly constant between T1 and T2 and that the vapor is close to ideal. These assumptions are often acceptable for moderate temperature spans and modest pressures. Near critical conditions, non-ideality and changing enthalpy reduce reliability.
The tool supports four modes: compute P2, compute T2, estimate ΔH, or back-calculate P1. Each mode rearranges the same integrated equation. For T2, it solves for 1/T2 using a logarithmic pressure ratio, then inverts it. That requires positive pressures and valid temperatures.
Pressures are converted to pascals internally and displayed in your selected unit, including kPa, bar, atm, mmHg, and psi. Temperatures may be entered in °C, K, or °F. When estimating ΔH, keep T1 and T2 separated; very small gaps amplify noise in (1/T2 - 1/T1).
Increasing temperature typically increases vapor pressure, so P2 rises as T2 rises when ΔH is positive. At fixed temperatures, a larger ΔH generally produces smaller pressure ratios. The result is most useful for relative shifts: how pressure changes between two temperatures, or what temperature matches a target pressure. Use the step list to confirm the pressure ratio and unit selections.
After calculation, results appear above the form for quick review. Export buttons create a CSV summary for spreadsheets and a PDF table for reports. For documentation, record your ΔH source, the units used, the temperature span, and both input points. For sensitive work, compare against published vapor-pressure curves.
Use it when you need a fast estimate of how equilibrium pressure changes with temperature during a phase change, or when you want a quick boiling-point or vapor-pressure comparison across two temperatures.
The equation uses absolute temperature. Converting to kelvin prevents offset errors that occur with Celsius or Fahrenheit and keeps the thermodynamic derivation valid for logarithmic relationships.
Enter molar latent heat for the transition you are modeling, often ΔHvap for evaporation. Use a value measured near your temperature range. If you only have mass-based data, convert it to per-mole using molar mass.
Yes. Select the ΔH mode and enter P1, P2, T1, and T2. The estimate is most reliable when the points are accurate, the temperature interval is moderate, and the substance behaves close to ideal in that range.
They occur when inputs imply a negative or invalid absolute temperature after rearranging the equation. This often results from swapped pressures, incorrect units, or using a latent heat value inconsistent with the temperature range.
Usually not. Near critical conditions, latent heat changes rapidly and vapor non-ideality becomes strong. For high accuracy, use substance-specific equations of state or published vapor-pressure correlations instead of this simplified relation.
The method uses ln(P2/P1), which is undefined for zero or negative pressures. Positive, consistent pressure units ensure the logarithm and exponential steps remain mathematically valid.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.