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Alpha-function for Peng–Robinson equation of state using reduced temperature Solution

STEP 0: Pre-Calculation Summary
Formula Used
alpha_function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2
α = (1+k*(1-sqrt(Tr)))^2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Pure Component Parameter- Pure Component Parameter is a function of 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
Pure Component Parameter: 1 --> No Conversion Required
Reduced Temperature: 0.131376 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
α = (1+k*(1-sqrt(Tr)))^2 --> (1+1*(1-sqrt(0.131376)))^2
Evaluating ... ...
α = 2.68154290615782
STEP 3: Convert Result to Output's Unit
2.68154290615782 --> No Conversion Required
FINAL ANSWER
2.68154290615782 <-- α-function
(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

Alpha-function for Peng–Robinson equation of state using reduced temperature Formula

alpha_function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2
α = (1+k*(1-sqrt(Tr)))^2

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 Alpha-function for Peng–Robinson equation of state using reduced temperature?

Alpha-function for Peng–Robinson equation of state using reduced temperature calculator uses alpha_function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2 to calculate the α-function, The Alpha-function for Peng–Robinson equation of state using reduced temperature formula is defined as a function of temperature and the acentric factor. α-function and is denoted by α symbol.

How to calculate Alpha-function for Peng–Robinson equation of state using reduced temperature using this online calculator? To use this online calculator for Alpha-function for Peng–Robinson equation of state using reduced temperature, enter Pure Component Parameter (k) and Reduced Temperature (Tr) and hit the calculate button. Here is how the Alpha-function for Peng–Robinson equation of state using reduced temperature calculation can be explained with given input values -> 2.681543 = (1+1*(1-sqrt(0.131376)))^2.

FAQ

What is Alpha-function for Peng–Robinson equation of state using reduced temperature?
The Alpha-function for Peng–Robinson equation of state using reduced temperature formula is defined as a function of temperature and the acentric factor and is represented as α = (1+k*(1-sqrt(Tr)))^2 or alpha_function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2. Pure Component Parameter is a function of 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 Alpha-function for Peng–Robinson equation of state using reduced temperature?
The Alpha-function for Peng–Robinson equation of state using reduced temperature formula is defined as a function of temperature and the acentric factor is calculated using alpha_function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2. To calculate Alpha-function for Peng–Robinson equation of state using reduced temperature, you need Pure Component Parameter (k) and Reduced Temperature (Tr). With our tool, you need to enter the respective value for Pure Component Parameter 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 α-function?
In this formula, α-function uses Pure Component Parameter 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
Where is the Alpha-function for Peng–Robinson equation of state using reduced temperature calculator used?
Among many, Alpha-function for Peng–Robinson equation of state using reduced temperature calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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