Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System Calculator

Ideal Gas Entropy Formula:

\[ S^{ig} = (y_1 \cdot S_1^{ig} + y_2 \cdot S_2^{ig}) - R \cdot (y_1 \cdot \ln(y_1) + y_2 \cdot \ln(y_2)) \]

Mole Fraction of Component 1 (y₁):

Ideal Gas Entropy of Component 1 (S₁ᶦᵍ):

J/kg·K

Mole Fraction of Component 2 (y₂):

Ideal Gas Entropy of Component 2 (S₂ᶦᵍ):

J/kg·K

Ideal Gas Entropy (Sᶦᵍ):

J/kg·K

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1. What is Ideal Gas Entropy in Binary System?

Definition: This calculator computes the entropy of an ideal gas mixture in a binary system using the ideal gas mixture model.

Purpose: It helps chemical engineers and researchers determine the entropy of gas mixtures for thermodynamic analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ S^{ig} = (y_1 \cdot S_1^{ig} + y_2 \cdot S_2^{ig}) - R \cdot (y_1 \cdot \ln(y_1) + y_2 \cdot \ln(y_2)) \]

Where:

\( S^{ig} \) — Ideal gas entropy of mixture (J/kg·K)
\( y_1 \) — Mole fraction of component 1 in vapour phase
\( S_1^{ig} \) — Ideal gas entropy of component 1 (J/kg·K)
\( y_2 \) — Mole fraction of component 2 in vapour phase
\( S_2^{ig} \) — Ideal gas entropy of component 2 (J/kg·K)
\( R \) — Universal gas constant (8.314 J/mol·K)

Explanation: The first part calculates the weighted average entropy, while the second part accounts for the entropy of mixing.

3. Importance of Ideal Gas Entropy Calculation

Details: Accurate entropy calculation is crucial for thermodynamic analysis, process design, and understanding system behavior in chemical engineering applications.

4. Using the Calculator

Tips: Enter mole fractions (must sum to ≤1), component entropies, and ensure all values are positive. Default values are provided for demonstration.

5. Frequently Asked Questions (FAQ)

Q1: Why does the entropy of mixing term appear?
A: The ln(y) terms account for the increased disorder when different gases mix, which contributes to the total entropy.

Q2: What if my mole fractions don't sum to 1?
A: The calculator will still work, but results may not be physically meaningful. For binary systems, y₁ + y₂ should typically equal 1.

Q3: Can I use this for non-ideal gases?
A: No, this calculator uses the ideal gas model. For real gases, additional correction terms would be needed.

Q4: What units should I use?
A: All entropy values should be in consistent units (J/kg·K shown here). The universal gas constant R is in J/mol·K.

Q5: How accurate is this calculation?
A: It's theoretically exact for ideal gas mixtures under the assumptions of the model.