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

✖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.ⓘ Critical Temperature [T_c]			+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%
✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [V_m,c]			+10% -10%
✖Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.ⓘ Reduced Molar Volume [V_m,r]			+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%
✖Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure [P_c]			+10% -10%
✖Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.ⓘ Reduced Pressure [P_r]			+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 given Reduced and Critical Parameters [α]

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

STEP 0: Pre-Calculation Summary

Formula Used

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 = ((([R]*(T_c*T_r))/((V_m,c*V_m,r)-b_PR))-(P_c*P_r))*(((V_m,c*V_m,r)^2)+(2*b_PR*(V_m,c*V_m,r))-(b_PR^2))/a_PR
This formula uses 1 Constants, 9 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.
Critical Temperature - (Measured in Kelvin) - 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.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
Critical Molar Volume - (Measured in Cubic Meter per Mole) - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.
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.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
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

Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
Reduced Temperature: 10 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Reduced Pressure: 3.675E-05 --> No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = ((([R]*(T_c*T_r))/((V_m,c*V_m,r)-b_PR))-(P_c*P_r))*(((V_m,c*V_m,r)^2)+(2*b_PR*(V_m,c*V_m,r))-(b_PR^2))/a_PR --> ((([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

Evaluating ... ...

α = 69479859.5267429

STEP 3: Convert Result to Output's Unit

69479859.5267429 --> No Conversion Required

FINAL ANSWER

69479859.5267429 ≈ 6.9E+7 <-- 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 given Reduced and Critical Parameters

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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 given Reduced and Critical Parameters 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 given Reduced and Critical Parameters?

Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters calculator 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 calculate 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 calculate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator 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. Here is how the Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 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.

FAQ

What is Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters?

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 and is represented as α = ((([R]*(T_c*T_r))/((V_m,c*V_m,r)-b_PR))-(P_c*P_r))*(((V_m,c*V_m,r)^2)+(2*b_PR*(V_m,c*V_m,r))-(b_PR^2))/a_PR or 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. 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, Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole, Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature, Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless & 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 given Reduced and Critical Parameters?

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 is calculated using 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 calculate Peng Robinson Alpha-Function using Peng Robinson Equation given Reduced and Critical Parameters, you need 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). With our tool, you need to enter the respective value for Critical Temperature, Reduced Temperature, Critical Molar Volume, Reduced Molar Volume, Peng–Robinson Parameter b, Critical Pressure, Reduced 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 Critical Temperature, Reduced Temperature, Critical Molar Volume, Reduced Molar Volume, Peng–Robinson Parameter b, Critical Pressure, Reduced Pressure & Peng–Robinson Parameter a. 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 = (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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