Slope of Coexistence Curve given Pressure and Latent Heat Calculator

Formula Used:

\[ \frac{dP}{dT} = \frac{P \times LH}{T^2 \times [R]} \]

Slope of Coexistence Curve (dP/dT):

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1. What is the Slope of Coexistence Curve?

Definition: The slope of the coexistence curve from the Clausius-Clapeyron equation (represented as dP/dT) is the slope of the tangent to the coexistence curve at any point.

Purpose: It describes how the pressure changes with temperature along the phase boundary between two phases of a substance.

2. How Does the Calculator Work?

The calculator uses the Clausius-Clapeyron equation:

\[ \frac{dP}{dT} = \frac{P \times LH}{T^2 \times [R]} \]

Where:

\( \frac{dP}{dT} \) — Slope of coexistence curve (Pa/K)
\( P \) — Pressure (Pa)
\( LH \) — Latent heat (J)
\( T \) — Temperature (K)
\( [R] \) — Universal gas constant (8.314 J/mol·K)

Explanation: The formula relates the slope of the phase boundary to the latent heat of the phase transition.

3. Importance of the Calculation

Details: Understanding the slope of coexistence curves is crucial in thermodynamics for predicting phase behavior and designing phase-change processes.

4. Using the Calculator

Tips: Enter the pressure in Pascals, latent heat in Joules, and temperature in Kelvin. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of dP/dT?
A: It shows how much pressure must change to maintain phase equilibrium when temperature changes.

Q2: What is typical latent heat value?
A: For water, latent heat of vaporization is about 2.26×10⁶ J/kg at 100°C.

Q3: Does this apply to all phase transitions?
A: This form applies to first-order phase transitions (liquid-vapor, solid-liquid).

Q4: Why is temperature squared in the denominator?
A: This comes from the thermodynamic derivation involving entropy changes.

Q5: What are typical units for dP/dT?
A: The slope is typically expressed in Pascals per Kelvin (Pa/K).