Alpha-function for Peng Robinson Equation of state given Reduced Temperature Calculator

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Peng Robinson Model of Real Gas

Berthelot and Modified Berthelot Model of Real Gas

Clausius Model of Real Gas

Redlich Kwong Model of Real Gas

Saturation Vapour Pressure

Specific Heat Capacity

Van der Waals Force

Wohl Model of Real Gas

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Critical Pressure

Critical Temperature

Peng Robinson Parameter

Reduced Pressure

Reduced Temperature

✖Pure Component Parameter is a function of the acentric factor.ⓘ Pure Component Parameter [k]			+10% -10%
✖Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.ⓘ Reduced Temperature [T_r]			+10% -10%

✖α-function is a function of temperature and the acentric factor.ⓘ Alpha-function for Peng Robinson Equation of state given Reduced Temperature [α]

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Formula

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Alpha-function for Peng Robinson Equation of state given Reduced Temperature

Formula

`"α" = (1+"k"*(1-sqrt("T"_{"r"})))^2`

Example

`"96.26334"=(1+"5"*(1-sqrt("10")))^2`

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Alpha-function for Peng Robinson Equation of state given Reduced Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2
α = (1+k*(1-sqrt(T_r)))^2
This formula uses 1 Functions, 3 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.
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: 5 --> No Conversion Required
Reduced Temperature: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = (1+k*(1-sqrt(T_r)))^2 --> (1+5*(1-sqrt(10)))^2

Evaluating ... ...

α = 96.2633403898973

STEP 3: Convert Result to Output's Unit

96.2633403898973 --> No Conversion Required

FINAL ANSWER

96.2633403898973 ≈ 96.26334 <-- 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 » Alpha-function for Peng Robinson Equation of state given Reduced Temperature

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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 Reduced Temperature Formula

α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2
α = (1+k*(1-sqrt(T_r)))^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 Reduced Temperature?

Alpha-function for Peng Robinson Equation of state given Reduced Temperature calculator uses α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2 to calculate the α-function, The Alpha-function for Peng Robinson Equation of state given Reduced 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 Reduced Temperature using this online calculator? To use this online calculator for Alpha-function for Peng Robinson Equation of state given Reduced Temperature, enter Pure Component Parameter (k) & Reduced Temperature (T_r) and hit the calculate button. Here is how the Alpha-function for Peng Robinson Equation of state given Reduced Temperature calculation can be explained with given input values -> 96.26334 = (1+5*(1-sqrt(10)))^2.

FAQ

What is Alpha-function for Peng Robinson Equation of state given Reduced Temperature?

The Alpha-function for Peng Robinson Equation of state given Reduced Temperature formula is defined as a function of temperature and the acentric factor and is represented as α = (1+k*(1-sqrt(T_r)))^2 or α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2. Pure Component Parameter is a function of the acentric factor & 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 given Reduced Temperature?

The Alpha-function for Peng Robinson Equation of state given Reduced Temperature formula is defined as a function of temperature and the acentric factor is calculated using α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2. To calculate Alpha-function for Peng Robinson Equation of state given Reduced Temperature, you need Pure Component Parameter (k) & Reduced Temperature (T_r). With our tool, you need to enter the respective value for Pure Component Parameter & 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 & Reduced 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( Temperature/Critical Temperature)))^2

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