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

GoPeng Robinson Alpha-Function using Peng Robinson Equation Formula

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

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

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}

α - α-function?T_c - Critical Temperature?T_r - Reduced Temperature?V_m,c - Critical Molar Volume?V_m,r - Reduced Molar Volume?b_PR - Peng–Robinson Parameter b?P_c - Critical Pressure?P_r - Reduced Pressure?a_PR - Peng–Robinson Parameter a?[R] - Universal gas constant?

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

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Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters equation looks like with Values.

Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters equation looks like with Units.

Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters equation looks like.

6.9E+7 = ((\frac{8.3145 \cdot (647 \cdot 10)}{(11.5 \cdot 11.2) - 0.12}) - (218 \cdot 3.7E-5)) \cdot \frac{({(11.5 \cdot 11.2)}^{2}) + (2 \cdot 0.12 \cdot (11.5 \cdot 11.2)) - ({0.12}^{2})}{0.1}

6.9E+7 = ((\frac{8.3145 \cdot (647K \cdot 10)}{(11.5m³/mol \cdot 11.2) - 0.12}) - (218Pa \cdot 3.7E-5)) \cdot \frac{({(11.5m³/mol \cdot 11.2)}^{2}) + (2 \cdot 0.12 \cdot (11.5m³/mol \cdot 11.2)) - ({0.12}^{2})}{0.1}

6.9E+7 = ((\frac{8.3145 \cdot (647 \cdot 10)}{(11.5 \cdot 11.2) - 0.12}) - (218 \cdot 3.7E-5)) \cdot \frac{({(11.5 \cdot 11.2)}^{2}) + (2 \cdot 0.12 \cdot (11.5 \cdot 11.2)) - ({0.12}^{2})}{0.1}

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

Follow our step by step solution on how to calculate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters?

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

α = ((\frac{[R] \cdot (647K \cdot 10)}{(11.5m³/mol \cdot 11.2) - 0.12}) - (218Pa \cdot 3.7E-5)) \cdot \frac{({(11.5m³/mol \cdot 11.2)}^{2}) + (2 \cdot 0.12 \cdot (11.5m³/mol \cdot 11.2)) - ({0.12}^{2})}{0.1}

Next Step Substitute values of Constants

∴

α = ((\frac{8.3145 \cdot (647K \cdot 10)}{(11.5m³/mol \cdot 11.2) - 0.12}) - (218Pa \cdot 3.7E-5)) \cdot \frac{({(11.5m³/mol \cdot 11.2)}^{2}) + (2 \cdot 0.12 \cdot (11.5m³/mol \cdot 11.2)) - ({0.12}^{2})}{0.1}

Next Step Prepare to Evaluate

∴

α = ((\frac{8.3145 \cdot (647 \cdot 10)}{(11.5 \cdot 11.2) - 0.12}) - (218 \cdot 3.7E-5)) \cdot \frac{({(11.5 \cdot 11.2)}^{2}) + (2 \cdot 0.12 \cdot (11.5 \cdot 11.2)) - ({0.12}^{2})}{0.1}

Next Step Evaluate

∴

α = 69479859.5267429

LAST Step Rounding Answer

∴

α = 6.9E+7

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

Variables

Constants

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

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

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

Critical Molar Volume

Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.

Symbol: V_m,c

Measurement: Molar Magnetic SusceptibilityUnit: m³/mol

Note: Value can be positive or negative.

Formulas to find Critical Molar Volume

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.

Symbol: V_m,r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Reduced Molar Volume

Peng–Robinson Parameter b

Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

Symbol: b_PR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Peng–Robinson Parameter b

Critical Pressure

Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.

Symbol: P_c

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Critical Pressure

Reduced Pressure

Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.

Symbol: P_r

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Reduced Pressure

Peng–Robinson Parameter a

Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

Symbol: a_PR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Peng–Robinson Parameter a

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

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 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})})

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters using this online evaluator? To use this online evaluator for Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters, enter Critical Temperature (T_c), Reduced Temperature (T_r), Critical Molar Volume (V_m,c), Reduced Molar Volume (V_m,r), Peng–Robinson Parameter b (b_PR), Critical Pressure (P_c), Reduced Pressure (P_r) & Peng–Robinson Parameter a (a_PR) and hit the calculate button.

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

What is the formula to find Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters?

The formula of Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters is expressed as 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. Here is an example- 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.

How to calculate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters?

With Critical Temperature (T_c), Reduced Temperature (T_r), Critical Molar Volume (V_m,c), Reduced Molar Volume (V_m,r), Peng–Robinson Parameter b (b_PR), Critical Pressure (P_c), Reduced Pressure (P_r) & Peng–Robinson Parameter a (a_PR) we can find Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters using the 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. This formula also uses Universal gas constant .

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

​GoPeng Robinson Alpha-Function using Peng Robinson Equation Formula

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

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

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

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

Other Formulas to find α-function

Other formulas in Peng Robinson Model of Real Gas category

How to Evaluate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters?

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

Variable Name

GoPeng Robinson Alpha-Function using Peng Robinson Equation Formula

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