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Peng Robinson Alpha-Function using Peng Robinson Equation Calculator

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✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]
+10%
-10%
✖Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure.ⓘ Molar Volume [Vm]
+10%
-10%
✖Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter b [bPR]
+10%
-10%
✖Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.ⓘ Pressure [p]
+10%
-10%
✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter a [aPR]
+10%
-10%
✖α-function is a function of temperature and the acentric factor.ⓘ Peng Robinson Alpha-Function using Peng Robinson Equation [α]
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Formula
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Peng Robinson Alpha-Function using Peng Robinson Equation

Formula
`"α" = ((("[R]"*"T")/("V"_{"m"}-"b"_{"PR"}))-"p")*(("V"_{"m"}^2)+(2*"b"_{"PR"}*"V"_{"m"})-("b"_{"PR"}^2))/"a"_{"PR"}`

Example
`"-3896112.070729"=((("[R]"*"85K")/("22.4m³/mol"-"0.12"))-"800Pa")*((("22.4m³/mol")^2)+(2*"0.12"*"22.4m³/mol")-(("0.12")^2))/"0.1"`

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Peng Robinson Alpha-Function using Peng Robinson Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
α = ((([R]*T)/(Vm-bPR))-p)*((Vm^2)+(2*bPR*Vm)-(bPR^2))/aPR
This formula uses 1 Constants, 6 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
α-function - α-function is a function of temperature and the acentric factor.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Molar Volume - (Measured in Cubic Meter per Mole) - Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Pressure - (Measured in Pascal) - Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Peng–Robinson Parameter a - Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
STEP 1: Convert Input(s) to Base Unit
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Molar Volume: 22.4 Cubic Meter per Mole --> 22.4 Cubic Meter per Mole No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Pressure: 800 Pascal --> 800 Pascal No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
α = ((([R]*T)/(Vm-bPR))-p)*((Vm^2)+(2*bPR*Vm)-(bPR^2))/aPR --> ((([R]*85)/(22.4-0.12))-800)*((22.4^2)+(2*0.12*22.4)-(0.12^2))/0.1
Evaluating ... ...
α = -3896112.07072938
STEP 3: Convert Result to Output's Unit
-3896112.07072938 --> No Conversion Required
FINAL ANSWER
-3896112.07072938 ≈ -3896112.070729 <-- α-function
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Peng Robinson Model of Real Gas » Peng Robinson Alpha-Function using Peng Robinson Equation

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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

Peng Robinson Alpha-Function using Peng Robinson Equation Formula

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
α = ((([R]*T)/(Vm-bPR))-p)*((Vm^2)+(2*bPR*Vm)-(bPR^2))/aPR

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 Peng Robinson Alpha-Function using Peng Robinson Equation?

Peng Robinson Alpha-Function using Peng Robinson Equation calculator uses 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 to calculate the α-function, The Peng Robinson alpha-function using Peng Robinson equation formula is defined as a function of temperature and the acentric factor. α-function is denoted by α symbol.

How to calculate Peng Robinson Alpha-Function using Peng Robinson Equation using this online calculator? To use this online calculator for Peng Robinson Alpha-Function using Peng Robinson Equation, enter Temperature (T), Molar Volume (Vm), Peng–Robinson Parameter b (bPR), Pressure (p) & Peng–Robinson Parameter a (aPR) and hit the calculate button. Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation calculation can be explained with given input values -> -3922866.788092 = ((([R]*85)/(22.4-0.12))-800)*((22.4^2)+(2*0.12*22.4)-(0.12^2))/0.1.

FAQ

What is Peng Robinson Alpha-Function using Peng Robinson Equation?
The Peng Robinson alpha-function using Peng Robinson equation formula is defined as a function of temperature and the acentric factor and is represented as α = ((([R]*T)/(Vm-bPR))-p)*((Vm^2)+(2*bPR*Vm)-(bPR^2))/aPR or 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. Temperature is the degree or intensity of heat present in a substance or object, Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed & Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
How to calculate Peng Robinson Alpha-Function using Peng Robinson Equation?
The Peng Robinson alpha-function using Peng Robinson equation formula is defined as a function of temperature and the acentric factor is calculated using 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. To calculate Peng Robinson Alpha-Function using Peng Robinson Equation, you need Temperature (T), Molar Volume (Vm), Peng–Robinson Parameter b (bPR), Pressure (p) & Peng–Robinson Parameter a (aPR). With our tool, you need to enter the respective value for Temperature, Molar Volume, Peng–Robinson Parameter b, Pressure & Peng–Robinson Parameter a 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 Temperature, Molar Volume, Peng–Robinson Parameter b, Pressure & Peng–Robinson Parameter a. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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
  • α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2
  • α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2
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