1. What is Slope of Coexistence Curve?

Definition: The slope of the coexistence curve from the Clausius-Clapeyron equation (dP/dT) represents how pressure changes with temperature along the phase boundary.

Purpose: This calculator helps determine the slope of the coexistence curve between two phases of a substance using enthalpy change, temperature, and volume change.

2. How Does the Calculator Work?

The calculator uses the Clausius-Clapeyron equation:

Where:

• \( \frac{dP}{dT} \) — Slope of coexistence curve (Pa/K)
• \( \Delta H \) — Enthalpy change of phase transition (J)
• \( T \) — Temperature at phase transition (K)
• \( \Delta V \) — Volume change during phase transition (m³)

Explanation: The slope indicates how much pressure must change to maintain phase equilibrium when temperature changes.

3. Importance of Slope Calculation

Details: Understanding this slope is crucial for phase diagram interpretation, predicting phase behavior, and designing phase transition processes.

4. Using the Calculator

Tips: Enter the enthalpy change in joules, temperature in kelvin, and volume change in cubic meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Clausius-Clapeyron equation used for?
A: It describes the relationship between pressure and temperature along a phase boundary (liquid-vapor, solid-liquid, etc.).

Q2: What are typical units for dP/dT?
A: The slope is typically expressed in pascals per kelvin (Pa/K) or atm/K.

Q3: When is this equation most accurate?
A: It's most accurate when the vapor phase behaves as an ideal gas and when ΔV is dominated by the vapor volume.

Q4: How do I find enthalpy change (ΔH)?
A: ΔH can be found experimentally or from thermodynamic tables for specific substances and phase transitions.

Q5: What does a steeper slope indicate?
A: A steeper slope means a larger pressure change is needed for a given temperature change to maintain phase equilibrium.