Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature Solution

STEP 0: Pre-Calculation Summary
Formula Used
α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2
α = (1+k*(1-sqrt( T/Tc)))^2
This formula uses 1 Functions, 4 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
α-function - α-function is a function of temperature and the acentric factor.
Pure Component Parameter - Pure Component Parameter is a function of the acentric factor.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
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.
STEP 1: Convert Input(s) to Base Unit
Pure Component Parameter: 5 --> No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
α = (1+k*(1-sqrt( T/Tc)))^2 --> (1+5*(1-sqrt( 85/647)))^2
Evaluating ... ...
α = 17.5369278782316
STEP 3: Convert Result to Output's Unit
17.5369278782316 --> No Conversion Required
FINAL ANSWER
17.5369278782316 17.53693 <-- α-function
(Calculation completed in 00.004 seconds)

Credits

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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

Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature Formula

α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2
α = (1+k*(1-sqrt( T/Tc)))^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 given Critical and Actual Temperature?

Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature calculator uses α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2 to calculate the α-function, The Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature formula is defined as a function of temperature and the acentric factor. α-function is denoted by α symbol.

How to calculate Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature using this online calculator? To use this online calculator for Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature, enter Pure Component Parameter (k), Temperature (T) & Critical Temperature (Tc) and hit the calculate button. Here is how the Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature calculation can be explained with given input values -> 17.53693 = (1+5*(1-sqrt( 85/647)))^2.

FAQ

What is Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature?
The Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature formula is defined as a function of temperature and the acentric factor and is represented as α = (1+k*(1-sqrt( T/Tc)))^2 or α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2. Pure Component Parameter is a function of the acentric factor, Temperature is the degree or intensity of heat present in a substance or object & 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.
How to calculate Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature?
The Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature formula is defined as a function of temperature and the acentric factor is calculated using α-function = (1+Pure Component Parameter*(1-sqrt( Temperature/Critical Temperature)))^2. To calculate Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature, you need Pure Component Parameter (k), Temperature (T) & Critical Temperature (Tc). With our tool, you need to enter the respective value for Pure Component Parameter, Temperature & Critical 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, Temperature & Critical Temperature. 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 = ((([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
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