Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
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 = ((([R]*(Tc*Tr))/((Vm,c*Vm,r)-bPR))-(Pc*Pr))*(((Vm,c*Vm,r)^2)+(2*bPR*(Vm,c*Vm,r))-(bPR^2))/aPR
This formula uses 1 Constants, 9 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.
Critical Temperature - (Measured in Kelvin) - Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
Critical Molar Volume - (Measured in Cubic Meter per Mole) - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.
Reduced Molar Volume - Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
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
Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
Reduced Temperature: 10 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Reduced Pressure: 3.675E-05 --> No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
α = ((([R]*(Tc*Tr))/((Vm,c*Vm,r)-bPR))-(Pc*Pr))*(((Vm,c*Vm,r)^2)+(2*bPR*(Vm,c*Vm,r))-(bPR^2))/aPR --> ((([R]*(647*10))/((11.5*11.2)-0.12))-(218*3.675E-05))*(((11.5*11.2)^2)+(2*0.12*(11.5*11.2))-(0.12^2))/0.1
Evaluating ... ...
α = 69479859.5267429
STEP 3: Convert Result to Output's Unit
69479859.5267429 --> No Conversion Required
FINAL ANSWER
69479859.5267429 6.9E+7 <-- α-function
(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

Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters Formula

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 = ((([R]*(Tc*Tr))/((Vm,c*Vm,r)-bPR))-(Pc*Pr))*(((Vm,c*Vm,r)^2)+(2*bPR*(Vm,c*Vm,r))-(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 given Reduced and Critical Parameters?

Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters calculator uses 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 to calculate the α-function, The Peng Robinson alpha-function using Peng Robinson equation given reduced and critical parameters 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 given Reduced and Critical Parameters using this online calculator? To use this online calculator for Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters, enter Critical Temperature (Tc), Reduced Temperature (Tr), Critical Molar Volume (Vm,c), Reduced Molar Volume (Vm,r), Peng–Robinson Parameter b (bPR), Critical Pressure (Pc), Reduced Pressure (Pr) & Peng–Robinson Parameter a (aPR) and hit the calculate button. Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 7E+7 = ((([R]*(647*10))/((11.5*11.2)-0.12))-(218*3.675E-05))*(((11.5*11.2)^2)+(2*0.12*(11.5*11.2))-(0.12^2))/0.1.

FAQ

What is Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters?
The Peng Robinson alpha-function using Peng Robinson equation given reduced and critical parameters formula is defined as a function of temperature and the acentric factor and is represented as α = ((([R]*(Tc*Tr))/((Vm,c*Vm,r)-bPR))-(Pc*Pr))*(((Vm,c*Vm,r)^2)+(2*bPR*(Vm,c*Vm,r))-(bPR^2))/aPR or 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. Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor, Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole, Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature, Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless & 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 given Reduced and Critical Parameters?
The Peng Robinson alpha-function using Peng Robinson equation given reduced and critical parameters formula is defined as a function of temperature and the acentric factor is calculated using 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. To calculate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters, you need Critical Temperature (Tc), Reduced Temperature (Tr), Critical Molar Volume (Vm,c), Reduced Molar Volume (Vm,r), Peng–Robinson Parameter b (bPR), Critical Pressure (Pc), Reduced Pressure (Pr) & Peng–Robinson Parameter a (aPR). With our tool, you need to enter the respective value for Critical Temperature, Reduced Temperature, Critical Molar Volume, Reduced Molar Volume, Peng–Robinson Parameter b, Critical Pressure, Reduced 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 Critical Temperature, Reduced Temperature, Critical Molar Volume, Reduced Molar Volume, Peng–Robinson Parameter b, Critical Pressure, Reduced Pressure & Peng–Robinson Parameter a. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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-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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