Pressure of Real Gas using Berthelot Equation given Critical and Reduced Parameters Calculator

Berthelot Equation Formula:

\[ p = \frac{[R] \times (T_r \times T_c)}{(V_{m,r} \times V_{m,c}) - b} - \frac{a}{(T_r \times T_c) \times ((V_{m,r} \times V_{m,c})^2)} \]

Reduced Temperature (T_r):

Critical Temperature (T_c) (K):

Reduced Molar Volume (V_m,r):

Critical Molar Volume (V_m,c) (m³/mol):

Berthelot Parameter a:

Berthelot Parameter b:

Pressure (Pa):

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1. What is the Berthelot Equation?

Definition: The Berthelot equation is a thermodynamic equation of state that modifies the ideal gas law to account for real gas behavior.

Purpose: It provides a more accurate calculation of pressure for real gases by including parameters for molecular size and intermolecular forces.

2. How Does the Calculator Work?

The calculator uses the Berthelot equation:

\[ p = \frac{[R] \times (T_r \times T_c)}{(V_{m,r} \times V_{m,c}) - b} - \frac{a}{(T_r \times T_c) \times ((V_{m,r} \times V_{m,c})^2)} \]

Where:

\( p \) — Pressure (Pa)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_r \) — Reduced Temperature (dimensionless)
\( T_c \) — Critical Temperature (K)
\( V_{m,r} \) — Reduced Molar Volume (dimensionless)
\( V_{m,c} \) — Critical Molar Volume (m³/mol)
\( a, b \) — Berthelot parameters specific to each gas

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

3. Importance of Berthelot Equation

Details: This equation provides more accurate pressure calculations for real gases, especially at moderate pressures and temperatures.

4. Using the Calculator

Tips: Enter all required parameters. Reduced temperature and volume are dimensionless ratios. Critical parameters and Berthelot constants are substance-specific.

5. Frequently Asked Questions (FAQ)

Q1: What are reduced temperature and volume?
A: Reduced parameters are ratios of actual values to critical values (T_r = T/T_c, V_r = V/V_c).

Q2: Where can I find Berthelot parameters?
A: These are typically found in thermodynamic tables or determined experimentally for specific gases.

Q3: What's the range of validity for this equation?
A: The Berthelot equation works best at moderate pressures, not too close to the critical point.

Q4: How does this differ from van der Waals equation?
A: The Berthelot equation uses a temperature-dependent term for attractive forces, while van der Waals uses a constant.

Q5: What units should I use?
A: Temperature in Kelvin, volume in m³/mol, pressure results in Pascals.