Critical Temperature given Clausius Parameter b, Reduced and Actual Parameters Calculator

Critical Temperature Formula:

\[ T'_c = \left(\frac{V_{real}}{V_r} - b'\right) \times \left(\frac{4 \times \frac{p}{P_r}}{[R]}\right) \]

Volume of Real Gas:

m³

Reduced Volume:

m³

Clausius Parameter b:

Pressure:

Reduced Pressure:

Critical Temperature (K):

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1. What is Critical Temperature in Clausius Model?

Definition: Critical temperature is the highest temperature at which the substance can exist as a liquid. At this point, phase boundaries vanish and the substance can exist both as a liquid and vapor.

Purpose: This calculator determines the critical temperature based on Clausius model parameters and actual/reduced properties of a real gas.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T'_c = \left(\frac{V_{real}}{V_r} - b'\right) \times \left(\frac{4 \times \frac{p}{P_r}}{[R]}\right) \]

Where:

\( T'_c \) — Critical temperature (Kelvin)
\( V_{real} \) — Volume of real gas (m³)
\( V_r \) — Reduced volume (dimensionless)
\( b' \) — Clausius parameter b for real gas
\( p \) — Pressure (Pascal)
\( P_r \) — Reduced pressure (dimensionless)
\( [R] \) — Universal gas constant (8.314 J/mol·K)

Explanation: The formula combines real gas properties with their reduced counterparts and the Clausius parameter to estimate the critical temperature.

3. Importance of Critical Temperature Calculation

Details: Knowing the critical temperature helps in understanding phase behavior, designing industrial processes, and predicting gas liquefaction conditions.

4. Using the Calculator

Tips: Enter the real gas volume, reduced volume, Clausius parameter b, pressure, and reduced pressure. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is reduced volume and pressure?
A: Reduced properties are the ratio of actual properties to critical properties (V_r = V/V_c, P_r = P/P_c).

Q2: What's the typical range for Clausius parameter b?
A: Parameter b depends on the gas but is typically small (0.001-0.1 m³/mol) representing molecular volume.

Q3: Why is universal gas constant used?
A: The constant relates energy, temperature, and quantity of substance in thermodynamic equations.

Q4: What units should be used?
A: Use SI units: m³ for volume, Pa for pressure, and Kelvin for temperature results.

Q5: How accurate is this calculation?
A: Accuracy depends on how well the Clausius model fits your real gas system.