Pressure of Real Gas using Berthelot Equation Calculator

Berthelot Equation Formula:

\[ p = \frac{[R] \times T}{V_m - b} - \frac{a}{T \times V_m^2} \]

Temperature (T):

Molar Volume (V_m):

m³/mol

Berthelot Parameter (a):

Berthelot Parameter (b):

Pressure (p):

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1. What is the Berthelot Equation?

Definition: The Berthelot equation is a thermodynamic equation of state for real gases that modifies the ideal gas law to account for molecular size and intermolecular forces.

Purpose: It provides a more accurate calculation of gas pressure under non-ideal conditions, especially at moderate pressures and temperatures.

2. How Does the Calculator Work?

The calculator uses the Berthelot equation:

\[ p = \frac{[R] \times T}{V_m - b} - \frac{a}{T \times V_m^2} \]

Where:

\( p \) — Pressure (Pascal)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T \) — Temperature (Kelvin)
\( V_m \) — Molar volume (m³/mol)
\( a \) — Berthelot parameter for intermolecular forces
\( b \) — Berthelot parameter for molecular volume

Explanation: The first term accounts for molecular volume exclusion, while the second term accounts for intermolecular attractive forces.

3. Importance of Berthelot Equation

Details: This equation provides better pressure estimates than the ideal gas law when dealing with real gases, especially in chemical engineering and physical chemistry applications.

4. Using the Calculator

Tips: Enter the temperature in Kelvin, molar volume in m³/mol, and Berthelot parameters a and b. All values must be positive (except parameters which can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Berthelot parameters?
A: Parameters vary by gas. For example, for nitrogen: a ≈ 0.136 Pa·m⁶/mol², b ≈ 3.86×10⁻⁵ m³/mol.

Q2: When is the Berthelot equation most accurate?
A: It works best at moderate pressures (not too high, not too low) and temperatures above the critical temperature.

Q3: How does this differ from van der Waals equation?
A: The Berthelot equation uses temperature-dependent attractive forces (a/T term) while van der Waals uses constant 'a'.

Q4: Can I use this for liquids?
A: No, the Berthelot equation is only valid for gases. Different equations are needed for liquids.

Q5: What units should I use?
A: Use Kelvin for temperature, m³/mol for molar volume, and SI-compatible units for parameters to get pressure in Pascals.