Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Reduced Temperature))
k = (sqrt(α)-1)/(1-sqrt(Tr))
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Pure Component Parameter - Pure Component Parameter is a function of the acentric factor.
α-function - α-function is a function of temperature and the acentric factor.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
STEP 1: Convert Input(s) to Base Unit
α-function: 2 --> No Conversion Required
Reduced Temperature: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k = (sqrt(α)-1)/(1-sqrt(Tr)) --> (sqrt(2)-1)/(1-sqrt(10))
Evaluating ... ...
k = -0.191563539689366
STEP 3: Convert Result to Output's Unit
-0.191563539689366 --> No Conversion Required
FINAL ANSWER
-0.191563539689366 -0.191564 <-- Pure Component Parameter
(Calculation completed in 00.004 seconds)

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20 Peng Robinson Model of Real Gas Calculators

Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters
Go α-function = ((([R]*(Critical Temperature*Reduced Temperature))/((Critical Molar Volume*Reduced Molar Volume)-Peng–Robinson Parameter b))-(Critical Pressure*Reduced Pressure))*(((Critical Molar Volume*Reduced Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Critical Molar Volume*Reduced Molar Volume))-(Peng–Robinson Parameter b^2))/Peng–Robinson Parameter a
Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters
Go Pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))
Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters
Go Temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R])
Temperature of Real Gas using Peng Robinson Equation
Go Temperature given CE = (Pressure+(((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))))*((Molar Volume-Peng–Robinson Parameter b)/[R])
Pressure of Real Gas using Peng Robinson Equation
Go Pressure = (([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))
Peng Robinson Alpha-Function using Peng Robinson Equation
Go α-function = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))/Peng–Robinson Parameter a
Actual Temperature given Peng Robinson Parameter a, and other Actual and Reduced Parameters
Go Temperature = Reduced Temperature*(sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2))))
Actual Temperature given Peng Robinson Parameter b, other Actual and Reduced Parameters
Go Temperature = Reduced Temperature*((Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R]))
Actual Pressure given Peng Robinson Parameter b, other Actual and Reduced Parameters
Go Pressure = Reduced Pressure*(0.07780*[R]*(Temperature/Reduced Temperature)/Peng–Robinson Parameter b)
Pure Component Factor for Peng Robinson Equation of state using Critical and Actual Temperature
Go Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Temperature/Critical Temperature))
Actual Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters
Go Pressure = Reduced Pressure*(0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a)
Actual Temperature given Peng Robinson parameter b, other reduced and critical parameters
Go Temperature given PRP = Reduced Temperature*((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))
Actual Temperature given Peng Robinson Parameter a, and other Reduced and Critical Parameters
Go Temperature = Reduced Temperature*(sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2))))
Actual Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter
Go Temperature = Critical Temperature*((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)
Actual Pressure given Peng Robinson Parameter b, other Reduced and Critical Parameters
Go Pressure = Reduced Pressure*(0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b)
Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature
Go α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2
Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature
Go Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Reduced Temperature))
Actual Pressure given Peng Robinson Parameter a, and other Reduced and Critical Parameters
Go Pressure given PRP = Reduced Pressure*(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)
Pure Component Factor for Peng Robinson Equation of state using Acentric Factor
Go Pure Component Parameter = 0.37464+(1.54226*Acentric Factor)-(0.26992*Acentric Factor*Acentric Factor)
Alpha-function for Peng Robinson Equation of state given Reduced Temperature
Go α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2

Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature Formula

Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Reduced Temperature))
k = (sqrt(α)-1)/(1-sqrt(Tr))

What are Real Gases?

Real gases are non ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behavior of real gases, the following must be taken into account:
- compressibility effects;
- variable specific heat capacity;
- van der Waals forces;
- non-equilibrium thermodynamic effects;
- issues with molecular dissociation and elementary reactions with variable composition.

How to Calculate Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature?

Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature calculator uses Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Reduced Temperature)) to calculate the Pure Component Parameter, The Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature formula is defined as a function of the acentric factor. Pure Component Parameter is denoted by k symbol.

How to calculate Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature using this online calculator? To use this online calculator for Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature, enter α-function (α) & Reduced Temperature (Tr) and hit the calculate button. Here is how the Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature calculation can be explained with given input values -> -0.191564 = (sqrt(2)-1)/(1-sqrt(10)).

FAQ

What is Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature?
The Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature formula is defined as a function of the acentric factor and is represented as k = (sqrt(α)-1)/(1-sqrt(Tr)) or Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Reduced Temperature)). α-function is a function of temperature and the acentric factor & Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
How to calculate Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature?
The Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature formula is defined as a function of the acentric factor is calculated using Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Reduced Temperature)). To calculate Pure Component Factor for Peng Robinson Equation of state using Reduced Temperature, you need α-function (α) & Reduced Temperature (Tr). With our tool, you need to enter the respective value for α-function & Reduced Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Pure Component Parameter?
In this formula, Pure Component Parameter uses α-function & Reduced Temperature. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Pure Component Parameter = (sqrt(α-function)-1)/(1-sqrt(Temperature/Critical Temperature))
  • Pure Component Parameter = 0.37464+(1.54226*Acentric Factor)-(0.26992*Acentric Factor*Acentric Factor)
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