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

✖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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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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< Peng Robinson Model of Real Gas Calculators

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

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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)))

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

LaTeX Go

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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