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## Credits

Lady Brabourne College (LBC), Kolkata
Prerana Bakli has created this Calculator and 500+ more calculators!
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## 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, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
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: 0.131376 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k = (sqrt(α)-1)/(1-sqrt(Tr)) --> (sqrt(2)-1)/(1-sqrt(0.131376))
Evaluating ... ...
k = 0.649704239158473
STEP 3: Convert Result to Output's Unit
0.649704239158473 --> No Conversion Required
FINAL ANSWER
0.649704239158473 <-- Pure Component Parameter
(Calculation completed in 00.000 seconds)

## < 10+ Peng–Robinson model of Real Gas Calculators

Peng–Robinson α-function using Peng–Robinson equation in terms of reduced and critical parameters
alpha_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 Go
Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters
critical_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))))/Reduced Pressure Go
Peng–Robinson parameter a using Peng–Robinson equation in terms of reduced and critical parameters
peng_robinson_parameter_a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))/α-function Go
Pressure of real gas using Peng–Robinson equation in terms of reduced and critical parameters
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))) Go
Temperature of real gas using Peng–Robinson equation in terms of reduced and critical parameters
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]) Go
Critical Pressure of real gas using Peng–Robinson equation in terms of reduced and actual parameters
critical_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))))/Reduced Pressure Go
Peng–Robinson α-function using Peng–Robinson equation
alpha_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 Go
Temperature of real gas using Peng–Robinson equation
temperature = (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]) Go
Pressure of real gas using Peng–Robinson equation
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))) Go
Peng–Robinson parameter a using Peng–Robinson equation
peng_robinson_parameter_a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/α-function Go

### 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 and 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) and 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 -> 0.649704 = (sqrt(2)-1)/(1-sqrt(0.131376)).

### 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 and 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) and Reduced Temperature (Tr). With our tool, you need to enter the respective value for α-function and 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 and Reduced Temperature. We can use 10 other way(s) to calculate the same, which is/are as follows -
• 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)))
• 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 = (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])
• 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])
• peng_robinson_parameter_a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/α-function
• peng_robinson_parameter_a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))/α-function
• alpha_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
• alpha_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
• critical_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))))/Reduced Pressure
• critical_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))))/Reduced Pressure
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