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Alpha-function for Peng Robinson Equation of state given Critical and Actual 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{\frac{T}{T c}}))}^{2}

α - α-function?k - Pure Component Parameter?T - Temperature?T_c - Critical Temperature?

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

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

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

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

17.5369 = {(1 + 5 \cdot (1 - \sqrt{\frac{85}{647}}))}^{2}

17.5369 = {(1 + 5 \cdot (1 - \sqrt{\frac{85K}{647K}}))}^{2}

17.5369 = {(1 + 5 \cdot (1 - \sqrt{\frac{85}{647}}))}^{2}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α = {(1 + 5 \cdot (1 - \sqrt{\frac{85K}{647K}}))}^{2}

Next Step Prepare to Evaluate

∴

α = {(1 + 5 \cdot (1 - \sqrt{\frac{85}{647}}))}^{2}

Next Step Evaluate

∴

α = 17.5369278782316

LAST Step Rounding Answer

∴

α = 17.5369

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

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Critical Temperature

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.

Symbol: T_c

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Critical 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 Reduced Temperature

α = {(1 + k \cdot (1 - \sqrt{T r}))}^{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 Critical and Actual Temperature?

Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature evaluator uses α-function = (1+Pure Component Parameter*(1-sqrt(Temperature/Critical Temperature)))^2 to evaluate 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 evaluate Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature using this online evaluator? To use this online evaluator for Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature, enter Pure Component Parameter (k), Temperature (T) & Critical Temperature (T_c) and hit the calculate button.

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

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

The formula of Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature is expressed as α-function = (1+Pure Component Parameter*(1-sqrt(Temperature/Critical Temperature)))^2. Here is an example- 17.53693 = (1+5*(1-sqrt(85/647)))^2.

How to calculate Alpha-function for Peng Robinson Equation of state given Critical and Actual Temperature?

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

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

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

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

FAQs on Alpha-function for Peng Robinson Equation of state given Critical and Actual 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