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

STEP 0: Pre-Calculation Summary
Formula Used
Ideal Gas Entropy = (Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Entropy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Entropy of Component 2)-[R]*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase))
Sig = (y1*S1ig+y2*S2ig)-[R]*(y1*ln(y1)+y2*ln(y2))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
Variables Used
Ideal Gas Entropy - (Measured in Joule per Kilogram K) - Ideal Gas entropy is the entropy in an ideal condition.
Mole Fraction of Component 1 in Vapour Phase - The mole fraction of component 1 in vapour phase can be defined as the ratio of the number of moles a component 1 to the total number of moles of components present in the vapour phase.
Ideal Gas Entropy of Component 1 - (Measured in Joule per Kilogram K) - Ideal Gas entropy of component 1 is the entropy of component 1 in an ideal condition.
Mole Fraction of Component 2 in Vapour Phase - The Mole Fraction of Component 2 in Vapour Phase can be defined as the ratio of the number of moles a component 2 to the total number of moles of components present in the vapour phase.
Ideal Gas Entropy of Component 2 - (Measured in Joule per Kilogram K) - Ideal Gas entropy of component 2 is the entropy of component 2 in an ideal condition.
STEP 1: Convert Input(s) to Base Unit
Mole Fraction of Component 1 in Vapour Phase: 0.5 --> No Conversion Required
Ideal Gas Entropy of Component 1: 87 Joule per Kilogram K --> 87 Joule per Kilogram K No Conversion Required
Mole Fraction of Component 2 in Vapour Phase: 0.55 --> No Conversion Required
Ideal Gas Entropy of Component 2: 77 Joule per Kilogram K --> 77 Joule per Kilogram K No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Sig = (y1*S1ig+y2*S2ig)-[R]*(y1*ln(y1)+y2*ln(y2)) --> (0.5*87+0.55*77)-[R]*(0.5*ln(0.5)+0.55*ln(0.55))
Evaluating ... ...
Sig = 91.4654545278143
STEP 3: Convert Result to Output's Unit
91.4654545278143 Joule per Kilogram K --> No Conversion Required
FINAL ANSWER
91.4654545278143 91.46545 Joule per Kilogram K <-- Ideal Gas Entropy
(Calculation completed in 00.004 seconds)

Credits

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Created by Shivam Sinha
National Institute Of Technology (NIT), Surathkal
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Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
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4 Ideal Gas Mixture Model Calculators

Ideal Gas Gibbs Free Energy using Ideal Gas Mixture Model in Binary System
​ Go Ideal Gas Gibbs Free Energy = modulus((Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Gibbs Free Energy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Gibbs Free Energy of Component 2)+[R]*Temperature*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase)))
Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System
​ Go Ideal Gas Entropy = (Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Entropy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Entropy of Component 2)-[R]*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase))
Ideal Gas Enthalpy using Ideal Gas Mixture Model in Binary System
​ Go Ideal Gas Enthalpy = Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Enthalpy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Enthalpy of Component 2
Ideal Gas Volume using Ideal Gas Mixture Model in Binary System
​ Go Ideal Gas Volume = Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Volume of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Volume of Component 2

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

Ideal Gas Entropy = (Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Entropy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Entropy of Component 2)-[R]*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase))
Sig = (y1*S1ig+y2*S2ig)-[R]*(y1*ln(y1)+y2*ln(y2))

Define Ideal Gas.

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions. Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles.

What is Duhem’s Theorem?

For any closed system formed from known amounts of prescribed chemical species, the equilibrium state is completely determined when any two independent variables are fixed. The two independent variables subject to specification may in general be either intensive or extensive. However, the number of independent intensive variables is given by the phase rule. Thus when F = 1, at least one of the two variables must be extensive, and when F = 0, both must be extensive.

How to Calculate Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System?

Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System calculator uses Ideal Gas Entropy = (Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Entropy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Entropy of Component 2)-[R]*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase)) to calculate the Ideal Gas Entropy, The Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System formula is defined as the function of ideal gas entropy of both components and mole fraction of both components in vapour phase in the binary system. Ideal Gas Entropy is denoted by Sig symbol.

How to calculate Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System using this online calculator? To use this online calculator for Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System, enter Mole Fraction of Component 1 in Vapour Phase (y1), Ideal Gas Entropy of Component 1 (S1ig), Mole Fraction of Component 2 in Vapour Phase (y2) & Ideal Gas Entropy of Component 2 (S2ig) and hit the calculate button. Here is how the Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System calculation can be explained with given input values -> 91.46545 = (0.5*87+0.55*77)-[R]*(0.5*ln(0.5)+0.55*ln(0.55)).

FAQ

What is Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System?
The Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System formula is defined as the function of ideal gas entropy of both components and mole fraction of both components in vapour phase in the binary system and is represented as Sig = (y1*S1ig+y2*S2ig)-[R]*(y1*ln(y1)+y2*ln(y2)) or Ideal Gas Entropy = (Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Entropy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Entropy of Component 2)-[R]*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase)). The mole fraction of component 1 in vapour phase can be defined as the ratio of the number of moles a component 1 to the total number of moles of components present in the vapour phase, Ideal Gas entropy of component 1 is the entropy of component 1 in an ideal condition, The Mole Fraction of Component 2 in Vapour Phase can be defined as the ratio of the number of moles a component 2 to the total number of moles of components present in the vapour phase & Ideal Gas entropy of component 2 is the entropy of component 2 in an ideal condition.
How to calculate Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System?
The Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System formula is defined as the function of ideal gas entropy of both components and mole fraction of both components in vapour phase in the binary system is calculated using Ideal Gas Entropy = (Mole Fraction of Component 1 in Vapour Phase*Ideal Gas Entropy of Component 1+Mole Fraction of Component 2 in Vapour Phase*Ideal Gas Entropy of Component 2)-[R]*(Mole Fraction of Component 1 in Vapour Phase*ln(Mole Fraction of Component 1 in Vapour Phase)+Mole Fraction of Component 2 in Vapour Phase*ln(Mole Fraction of Component 2 in Vapour Phase)). To calculate Ideal Gas Entropy using Ideal Gas Mixture Model in Binary System, you need Mole Fraction of Component 1 in Vapour Phase (y1), Ideal Gas Entropy of Component 1 (S1ig), Mole Fraction of Component 2 in Vapour Phase (y2) & Ideal Gas Entropy of Component 2 (S2ig). With our tool, you need to enter the respective value for Mole Fraction of Component 1 in Vapour Phase, Ideal Gas Entropy of Component 1, Mole Fraction of Component 2 in Vapour Phase & Ideal Gas Entropy of Component 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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