Clausius–Clapeyron Equation Calculator

Clausius–Clapeyron Calculator

The Clausius–Clapeyron Equation

The Clausius–Clapeyron equation is a fundamental relationship in thermodynamics and physical chemistry that describes how the vapor pressure of a liquid (or solid) changes with temperature. It's derived based on the assumption that the phase transition follows certain ideal conditions.

This calculator uses the two-point form of the equation, which is useful for practical calculations when you know the vapor pressure at one temperature and want to find it at another, or if you want to determine the enthalpy of vaporization from two pressure-temperature data points.

ln(P₂/P₁) = -ΔHvap/R * (1/T₂ - 1/T₁)

Where:
• P₁ and P₂ = Vapor pressures at temperatures T₁ and T₂, respectively.
• T₁ and T₂ = Absolute temperatures (in Kelvin).
• ΔHvap = Enthalpy of vaporization of the substance (energy needed to vaporize one mole).
• R = The Ideal Gas Constant (8.314 J/mol·K).

Frequently Asked Questions

What are the assumptions of the Clausius–Clapeyron equation?

The derivation of this equation makes several key assumptions:
• The vapor phase behaves like an ideal gas.
• The volume of the liquid phase is negligible compared to the volume of the vapor phase.
• The enthalpy of vaporization (ΔHvap) is constant over the temperature range considered (this is often a reasonable approximation over small temperature ranges).
• The system is at equilibrium between the liquid and vapor phases.
These assumptions mean the equation is most accurate at temperatures well below the critical point and at moderate pressures.

How is this equation used in the real world?

The Clausius–Clapeyron relation has many practical applications, including:
• Predicting boiling points: By setting P₂ to atmospheric pressure (e.g., 1 atm), you can calculate the temperature (T₂) at which a liquid will boil at that pressure if you know its vapor pressure at another temperature (T₁) and its ΔHvap.
• Estimating enthalpy of vaporization: If you measure the vapor pressure of a liquid at two different temperatures, you can use this equation to calculate its ΔHvap.
• Meteorology: Understanding how the saturation vapor pressure of water changes with temperature is crucial for predicting weather phenomena like cloud formation and dew point.
• Engineering: Designing distillation columns, refrigeration cycles, and other processes involving phase changes.

Why must I use Kelvin for temperature?

The Clausius–Clapeyron equation, like many thermodynamic relationships, is derived based on absolute temperature scales where zero corresponds to the theoretical minimum energy state (absolute zero). The Kelvin scale is the standard absolute scale used in science. Using Celsius or Fahrenheit directly in the 1/T terms would lead to incorrect results and potentially division by zero if 0°C or 0°F were used. This calculator automatically converts temperatures to Kelvin before performing calculations.