Temperature using Modified Berthelot Equation given Reduced and Actual Parameters Calculator

Temperature Formula:

\[ T = \frac{p \times V_m}{[R]} \div \left(1 + \left(\frac{9P_r}{128T_r}\right) \times \left(1 - \frac{6}{T_r^2}\right)\right) \]

Pressure:

Molar Volume:

m³/mol

Reduced Pressure:

Reduced Temperature:

Temperature (K):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Modified Berthelot Equation?

Definition: The Modified Berthelot Equation is a thermodynamic equation of state that relates temperature, pressure, and volume of real gases with correction factors.

Purpose: It provides more accurate temperature calculations for real gases compared to the ideal gas law, especially under high pressure or low temperature conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = \frac{p \times V_m}{[R]} \div \left(1 + \left(\frac{9P_r}{128T_r}\right) \times \left(1 - \frac{6}{T_r^2}\right)\right) \]

Where:

\( T \) — Temperature (Kelvin)
\( p \) — Pressure (Pascal)
\( V_m \) — Molar Volume (m³/mol)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( P_r \) — Reduced Pressure (dimensionless)
\( T_r \) — Reduced Temperature (dimensionless)

Explanation: The numerator calculates the ideal gas temperature, while the denominator applies corrections for real gas behavior based on reduced properties.

3. Importance of Accurate Temperature Calculation

Details: Precise temperature determination is crucial for chemical engineering processes, thermodynamic studies, and industrial applications involving gases under non-ideal conditions.

4. Using the Calculator

Tips: Enter the pressure in Pascals, molar volume in m³/mol, reduced pressure (dimensionless), and reduced temperature (dimensionless). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are reduced pressure and temperature?
A: Reduced properties are ratios of actual properties to critical properties (P/P_critical and T/T_critical).

Q2: When is the Modified Berthelot Equation most accurate?
A: It works best for moderate pressure ranges and temperatures not too close to the critical point.

Q3: How do I find reduced properties?
A: Divide the actual property by its critical value for the specific gas (available in thermodynamic tables).

Q4: What's the difference from the ideal gas law?
A: This equation includes correction terms for intermolecular forces and molecular volume effects.

Q5: Can I use this for liquids?
A: No, this equation is specifically designed for gaseous systems.