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

GoPeng Robinson Alpha-Function using Peng Robinson Equation Formula

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

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α-function is a function of temperature and the acentric factor. Check FAQs

α = {(1 + k \cdot (1 - \sqrt{T r}))}^{2}

α - α-function?k - Pure Component Parameter?T_r - Reduced Temperature?

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

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Here is how the Alpha-function for Peng Robinson Equation of state given Reduced Temperature equation looks like with Values.

Here is how the Alpha-function for Peng Robinson Equation of state given Reduced Temperature equation looks like with Units.

Here is how the Alpha-function for Peng Robinson Equation of state given Reduced Temperature equation looks like.

96.2633 = {(1 + 5 \cdot (1 - \sqrt{10}))}^{2}

96.2633 = {(1 + 5 \cdot (1 - \sqrt{10}))}^{2}

96.2633 = {(1 + 5 \cdot (1 - \sqrt{10}))}^{2}

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

Follow our step by step solution on how to calculate Alpha-function for Peng Robinson Equation of state given Reduced Temperature?

FIRST Step Consider the formula

α = {(1 + k \cdot (1 - \sqrt{T r}))}^{2}

Next Step Substitute values of Variables

∴

α = {(1 + 5 \cdot (1 - \sqrt{10}))}^{2}

Next Step Prepare to Evaluate

∴

α = {(1 + 5 \cdot (1 - \sqrt{10}))}^{2}

Next Step Evaluate

∴

α = 96.2633403898973

LAST Step Rounding Answer

∴

α = 96.2633

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

Variables

Functions

α-function

α-function is a function of temperature and the acentric factor.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find α-function

Pure Component Parameter

Pure Component Parameter is a function of the acentric factor.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Pure Component Parameter

Reduced Temperature

Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.

Symbol: T_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Reduced Temperature

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.

Syntax: sqrt(Number)

Other Formulas to find α-function

Go Peng Robinson Alpha-Function using Peng Robinson Equation

α = ((\frac{[R] \cdot T}{V m - b PR}) - p) \cdot \frac{({V m}^{2}) + (2 \cdot b PR \cdot V m) - ({b PR}^{2})}{a PR}

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

α = ((\frac{[R] \cdot (T c \cdot T r)}{(V m,c \cdot V m,r) - b PR}) - (P c \cdot P r)) \cdot \frac{({(V m,c \cdot V m,r)}^{2}) + (2 \cdot b PR \cdot (V m,c \cdot V m,r)) - ({b PR}^{2})}{a PR}

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

α = {(1 + k \cdot (1 - \sqrt{\frac{T}{T c}}))}^{2}

Other formulas in Peng Robinson Model of Real Gas category

Go Pressure of Real Gas using Peng Robinson Equation

p = (\frac{[R] \cdot T}{V m - b PR}) - (\frac{a PR \cdot α}{({V m}^{2}) + (2 \cdot b PR \cdot V m) - ({b PR}^{2})})

Go Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

p = (\frac{[R] \cdot (T r \cdot T c)}{(V m,r \cdot V m,c) - b PR}) - (\frac{a PR \cdot α}{({(V m,r \cdot V m,c)}^{2}) + (2 \cdot b PR \cdot (V m,r \cdot V m,c)) - ({b PR}^{2})})

Go Temperature of Real Gas using Peng Robinson Equation

T CE = (p + ((\frac{a PR \cdot α}{({V m}^{2}) + (2 \cdot b PR \cdot V m) - ({b PR}^{2})}))) \cdot (\frac{V m - b PR}{[R]})

Go Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

T = ((P r \cdot P c) + ((\frac{a PR \cdot α}{({(V m,r \cdot V m,c)}^{2}) + (2 \cdot b PR \cdot (V m,r \cdot V m,c)) - ({b PR}^{2})}))) \cdot (\frac{(V m,r \cdot V m,c) - b PR}{[R]})

How to Evaluate Alpha-function for Peng Robinson Equation of state given Reduced Temperature?

Alpha-function for Peng Robinson Equation of state given Reduced Temperature evaluator uses α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2 to evaluate 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 evaluate Alpha-function for Peng Robinson Equation of state given Reduced Temperature using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Alpha-function for Peng Robinson Equation of state given Reduced Temperature?

The formula of Alpha-function for Peng Robinson Equation of state given Reduced Temperature is expressed as α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2. Here is an example- 96.26334 = (1+5*(1-sqrt(10)))^2.

How to calculate Alpha-function for Peng Robinson Equation of state given Reduced Temperature?

With Pure Component Parameter (k) & Reduced Temperature (T_r) we can find Alpha-function for Peng Robinson Equation of state given Reduced Temperature using the formula - α-function = (1+Pure Component Parameter*(1-sqrt(Reduced Temperature)))^2. This formula also uses Square Root Function function(s).

What are the other ways to Calculate α-function?

Here are the different ways to Calculate α-function-

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

​GoPeng Robinson Alpha-Function using Peng Robinson Equation Formula

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

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

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

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

Other Formulas to find α-function

Other formulas in Peng Robinson Model of Real Gas category

How to Evaluate Alpha-function for Peng Robinson Equation of state given Reduced Temperature?

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

Variable Name

GoPeng Robinson Alpha-Function using Peng Robinson Equation Formula

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