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

Reduced Pressure Formula (Clausius Equation):

\[ P_r = \frac{\left(\frac{[R] \times (T_r \times T'_c)}{(V'_m \times V_c - b')} - \frac{a}{(T_r \times T'_c) \times ((V'_m \times V_c + c)^2)}\right)}{P'_c} \]

Reduced Temperature (Tr):

Critical Temperature (T'c):

Reduced Molar Volume (V'm,r):

Critical Volume (Vc):

m³

Clausius Parameter b:

Clausius Parameter a:

Clausius Parameter c:

Critical Pressure (P'c):

Reduced Pressure (Pr):

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1. What is Reduced Pressure in Clausius Equation?

Definition: Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is a dimensionless quantity used in corresponding states theory.

Purpose: This calculator computes the reduced pressure of a real gas using the Clausius equation of state, which accounts for deviations from ideal gas behavior.

2. How Does the Calculator Work?

The calculator uses the Clausius equation formula:

\[ P_r = \frac{\left(\frac{[R] \times (T_r \times T'_c)}{(V'_m \times V_c - b')} - \frac{a}{(T_r \times T'_c) \times ((V'_m \times V_c + c)^2)}\right)}{P'_c} \]

Where:

\( P_r \) — Reduced Pressure (dimensionless)
\( T_r \) — Reduced Temperature (dimensionless)
\( T'_c \) — Critical Temperature (K)
\( V'_m \) — Reduced Molar Volume (dimensionless)
\( V_c \) — Critical Volume (m³)
\( b' \) — Clausius Parameter b
\( a \) — Clausius Parameter a
\( c \) — Clausius Parameter c
\( P'_c \) — Critical Pressure (Pa)
\( [R] \) — Universal gas constant (8.314 J/mol·K)

3. Importance of Reduced Pressure Calculation

Details: Calculating reduced pressure helps in understanding gas behavior under various conditions and is essential for thermodynamic calculations in engineering applications.

4. Using the Calculator

Tips: Enter all required parameters. The reduced temperature and reduced molar volume are dimensionless. Critical parameters and Clausius parameters should be in appropriate units.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Clausius parameters?
A: These are substance-specific empirical parameters that must be determined experimentally for each gas.

Q2: Why use reduced parameters?
A: Reduced parameters allow for generalized correlations that can be applied to many substances.

Q3: What's the range for reduced pressure?
A: Typically between 0 and 1, but can exceed 1 for supercritical conditions.

Q4: How accurate is the Clausius equation?
A: It's more accurate than ideal gas law but still an approximation - accuracy depends on the substance and conditions.

Q5: Where can I find critical parameters for gases?
A: They are available in thermodynamic reference tables for common substances.