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

Reduced Pressure Formula:

\[ P_r = \frac{\left(\frac{[R] \times T_{rg}}{V'_m - b'}\right) - \left(\frac{a}{T_{rg} \times (V'_m + c)^2}\right)}{P'_c} \]

Temperature of Real Gas (K):

Molar Volume of Real Gas (m³):

Clausius Parameter b:

Clausius Parameter a:

Clausius Parameter c:

Critical Pressure (Pa):

Reduced Pressure:

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1. What is Reduced Pressure of Real Gas?

Definition: Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.

Purpose: It helps in the study of real gases using the principle of corresponding states.

2. How Does the Calculator Work?

The calculator uses the Clausius equation:

\[ P_r = \frac{\left(\frac{[R] \times T_{rg}}{V'_m - b'}\right) - \left(\frac{a}{T_{rg} \times (V'_m + c)^2}\right)}{P'_c} \]

Where:

\( P_r \) — Reduced Pressure (dimensionless)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{rg} \) — Temperature of real gas (K)
\( V'_m \) — Molar volume of real gas (m³)
\( b' \) — Clausius Parameter b
\( a \) — Clausius Parameter a
\( c \) — Clausius Parameter c
\( P'_c \) — Critical Pressure (Pa)

3. Importance of Reduced Pressure Calculation

Details: Calculating reduced pressure helps predict the behavior of real gases under various conditions and is essential in thermodynamics and chemical engineering applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Temperature must be in Kelvin, molar volume in cubic meters, and critical pressure in Pascals.

5. Frequently Asked Questions (FAQ)

Q1: What is the Clausius equation used for?
A: The Clausius equation is a thermodynamic equation of state used to describe the behavior of real gases.

Q2: Why is reduced pressure dimensionless?
A: Because it's a ratio of two pressures (actual pressure divided by critical pressure), the units cancel out.

Q3: What are typical values for Clausius parameters?
A: These vary by gas. For example, for CO₂: a ≈ 3.592, b ≈ 0.04267, c ≈ 0 (in appropriate units).

Q4: How do I find critical pressure for a substance?
A: Critical pressure is a physical property that can be found in chemical engineering handbooks or material safety data sheets.

Q5: What's the difference between ideal and real gas behavior?
A: Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and molecular volume.