Critical Pressure given Clausius Parameter c, Reduced and Actual Parameters Calculator

Critical Pressure Formula:

\[ P'_c = \frac{3[R](\frac{T_{rg}}{T_r})}{8(c + \frac{V_{real}}{V_r})} \]

Temperature of Real Gas:

Reduced Temperature:

Clausius Parameter c:

Volume of Real Gas:

m³

Reduced Volume:

m³

Critical Pressure of Real Gas (Pa):

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1. What is Critical Pressure given Clausius Parameter c?

Definition: This calculator determines the critical pressure of a real gas using the Clausius parameter c along with reduced and actual temperature and volume parameters.

Purpose: It helps in thermodynamic calculations and understanding gas behavior near critical points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P'_c = \frac{3[R](\frac{T_{rg}}{T_r})}{8(c + \frac{V_{real}}{V_r})} \]

Where:

\( P'_c \) — Critical Pressure of Real Gas (Pascal)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{rg} \) — Temperature of Real Gas (Kelvin)
\( T_r \) — Reduced Temperature (dimensionless)
\( c \) — Clausius Parameter c (empirical constant)
\( V_{real} \) — Volume of Real Gas (m³)
\( V_r \) — Reduced Volume (m³)

Explanation: The formula relates the critical pressure to temperature and volume parameters through the Clausius equation of state.

3. Importance of Critical Pressure Calculation

Details: Critical pressure is essential for understanding phase behavior, designing chemical processes, and predicting gas-liquid transitions.

4. Using the Calculator

Tips: Enter all required parameters with positive values. Temperature should be in Kelvin, volumes in cubic meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the Clausius parameter c?
A: It's an empirical parameter characteristic to the equation obtained from Clausius model of real gas.

Q2: How do I get reduced temperature and volume?
A: Reduced parameters are the actual values divided by their critical point values (T/Tc, V/Vc).

Q3: What units does this calculator use?
A: Temperature in Kelvin, volumes in cubic meters, pressure in Pascals.

Q4: When is this calculation most useful?
A: For real gases at high pressures or near critical points where ideal gas law fails.

Q5: What's a typical range for Clausius parameter c?
A: It varies by substance but is typically a small positive number (often 0.001 to 0.1).