Peng Robinson Alpha-Function using Peng Robinson Equation Calculator

✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%
✖Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure.ⓘ Molar Volume [V_m]			+10% -10%
✖Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter b [b_PR]			+10% -10%
✖Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.ⓘ Pressure [p]			+10% -10%
✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter a [a_PR]			+10% -10%

✖α-function is a function of temperature and the acentric factor.ⓘ Peng Robinson Alpha-Function using Peng Robinson Equation [α]

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Peng Robinson Alpha-Function using Peng Robinson Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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 = ((([R]*T)/(V_m-b_PR))-p)*((V_m^2)+(2*b_PR*V_m)-(b_PR^2))/a_PR
This formula uses 1 Constants, 6 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

α-function - α-function is a function of temperature and the acentric factor.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Molar Volume - (Measured in Cubic Meter per Mole) - Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Pressure - (Measured in Pascal) - Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Peng–Robinson Parameter a - Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

STEP 1: Convert Input(s) to Base Unit

Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Molar Volume: 22.4 Cubic Meter per Mole --> 22.4 Cubic Meter per Mole No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Pressure: 800 Pascal --> 800 Pascal No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = ((([R]*T)/(V_m-b_PR))-p)*((V_m^2)+(2*b_PR*V_m)-(b_PR^2))/a_PR --> ((([R]*85)/(22.4-0.12))-800)*((22.4^2)+(2*0.12*22.4)-(0.12^2))/0.1

Evaluating ... ...

α = -3896112.07072938

STEP 3: Convert Result to Output's Unit

-3896112.07072938 --> No Conversion Required

FINAL ANSWER

-3896112.07072938 ≈ -3896112.070729 <-- 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 » Peng Robinson Alpha-Function using Peng Robinson Equation

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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)))

Peng Robinson Alpha-Function using Peng Robinson Equation Formula

LaTeX Go

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 Peng Robinson Alpha-Function using Peng Robinson Equation?

Peng Robinson Alpha-Function using Peng Robinson Equation calculator uses 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 to calculate the α-function, The Peng Robinson alpha-function using Peng Robinson equation formula is defined as a function of temperature and the acentric factor. α-function is denoted by α symbol.

How to calculate Peng Robinson Alpha-Function using Peng Robinson Equation using this online calculator? To use this online calculator for Peng Robinson Alpha-Function using Peng Robinson Equation, enter Temperature (T), Molar Volume (V_m), Peng–Robinson Parameter b (b_PR), Pressure (p) & Peng–Robinson Parameter a (a_PR) and hit the calculate button. Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation calculation can be explained with given input values -> -3922866.788092 = ((([R]*85)/(22.4-0.12))-800)*((22.4^2)+(2*0.12*22.4)-(0.12^2))/0.1.

FAQ

What is Peng Robinson Alpha-Function using Peng Robinson Equation?

The Peng Robinson alpha-function using Peng Robinson equation formula is defined as a function of temperature and the acentric factor and is represented as α = ((([R]*T)/(V_m-b_PR))-p)*((V_m^2)+(2*b_PR*V_m)-(b_PR^2))/a_PR or 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. Temperature is the degree or intensity of heat present in a substance or object, Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed & Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

How to calculate Peng Robinson Alpha-Function using Peng Robinson Equation?

The Peng Robinson alpha-function using Peng Robinson equation formula is defined as a function of temperature and the acentric factor is calculated using 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. To calculate Peng Robinson Alpha-Function using Peng Robinson Equation, you need Temperature (T), Molar Volume (V_m), Peng–Robinson Parameter b (b_PR), Pressure (p) & Peng–Robinson Parameter a (a_PR). With our tool, you need to enter the respective value for Temperature, Molar Volume, Peng–Robinson Parameter b, Pressure & Peng–Robinson Parameter a 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 Temperature, Molar Volume, Peng–Robinson Parameter b, Pressure & Peng–Robinson Parameter a. We can use 3 other way(s) to calculate the same, which is/are as follows -

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
α-function = (1+Pure Component Parameter*(1-sqrt(Temperature/Critical Temperature)))^2

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