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

Critical Temperature Formula:

\[ T_c = \frac{(c + \frac{V_{real}}{V_r}) \times 8 \times \frac{p}{P_r}}{3 \times R} \]

Clausius Parameter c:

Volume of Real Gas (m³):

Reduced Volume (m³):

Pressure (Pa):

Reduced Pressure:

Critical Temperature (K):

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1. What is Critical Temperature?

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

Purpose: This calculator determines the critical temperature using Clausius parameters and reduced/actual properties of real gases.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_c = \frac{(c + \frac{V_{real}}{V_r}) \times 8 \times \frac{p}{P_r}}{3 \times R} \]

Where:

\( T_c \) — Critical temperature (Kelvin)
\( c \) — Clausius parameter c (empirical parameter)
\( V_{real} \) — Volume of real gas (m³)
\( V_r \) — Reduced volume (m³)
\( p \) — Pressure (Pascal)
\( P_r \) — Reduced pressure (dimensionless)
\( R \) — Universal gas constant (8.314 J/mol·K)

Explanation: The formula combines Clausius parameters with reduced and actual properties to estimate the critical temperature of a real gas.

3. Importance of Critical Temperature

Details: Knowing the critical temperature is essential for understanding phase behavior, designing chemical processes, and working with supercritical fluids.

4. Using the Calculator

Tips: Enter the Clausius parameter c, volume of real gas, reduced volume, pressure, and reduced pressure. All values must be > 0 (except c which can be 0).

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 find reduced properties?
A: Reduced properties are the actual property divided by the critical property of the substance (P_r = P/P_c, V_r = V/V_c).

Q3: What units should I use?
A: Use SI units: m³ for volumes, Pa for pressure. Temperature result is in Kelvin.

Q4: Can this be used for all gases?
A: This is specific to the Clausius model of real gases. Accuracy may vary for different substances.

Q5: What's a typical range for critical temperatures?
A: Critical temperatures vary widely: from 33K for hydrogen to 647K for water, and higher for complex molecules.