Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters Calculator

✖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.ⓘ α-function [α]			+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%
✖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%

✖Real Gas Temperature is the degree or intensity of heat present in a substance or object.ⓘ Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters [T_real]

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Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters Solution

STEP 0: Pre-Calculation Summary

Formula Used

Real Gas Temperature = ((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]))/Reduced Temperature
T_real = ((p+(((a_PR*α)/((V_m^2)+(2*b_PR*V_m)-(b_PR^2)))))*((V_m-b_PR)/[R]))/T_r
This formula uses 1 Constants, 7 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Real Gas Temperature - (Measured in Kelvin) - Real Gas Temperature is the degree or intensity of heat present in a substance or object.
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.
α-function - α-function is a function of temperature and the acentric factor.
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.
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

Pressure: 800 Pascal --> 800 Pascal No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
α-function: 2 --> 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
Reduced Temperature: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_real = ((p+(((a_PR*α)/((V_m^2)+(2*b_PR*V_m)-(b_PR^2)))))*((V_m-b_PR)/[R]))/T_r --> ((800+(((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2)))))*((22.4-0.12)/[R]))/10

Evaluating ... ...

T_real = 214.373551309635

STEP 3: Convert Result to Output's Unit

214.373551309635 Kelvin --> No Conversion Required

FINAL ANSWER

214.373551309635 ≈ 214.3736 Kelvin <-- Real Gas Temperature

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Critical Temperature Calculators

Critical Temperature given Peng Robinson Parameter a, and other Actual and Reduced Parameters

LaTeX Go Critical Temperature = sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2)))

Critical Temperature given Peng Robinson Parameter b and other Actual and Reduced Parameters

LaTeX Go Critical Temperature = (Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R])

Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter

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

Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter a

LaTeX Go Critical Temperature = sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2)))

< Important Formulae on Different Models of Real Gas Calculators

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])

Critical Pressure given Peng Robinson Parameter b and other Actual and Reduced Parameters

LaTeX Go Critical Pressure given PRP = 0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b

Actual Temperature given Peng Robinson parameter b, other reduced and critical parameters

LaTeX Go Temperature given PRP = Reduced Temperature*((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))

Actual Pressure given Peng Robinson Parameter a, and other Reduced and Critical Parameters

LaTeX Go Pressure given PRP = Reduced Pressure*(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)

Critical Temperature using Peng Robinson Equation given Reduced and Actual 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 Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters?

Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters calculator uses Real Gas Temperature = ((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]))/Reduced Temperature to calculate the Real Gas Temperature, The Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters formula is defined as the highest temperature at which the substance can exist as a liquid. Real Gas Temperature is denoted by T_real symbol.

How to calculate Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters using this online calculator? To use this online calculator for Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters, enter Pressure (p), Peng–Robinson Parameter a (a_PR), α-function (α), Molar Volume (V_m), Peng–Robinson Parameter b (b_PR) & Reduced Temperature (T_r) and hit the calculate button. Here is how the Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters calculation can be explained with given input values -> 214.3736 = ((800+(((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2)))))*((22.4-0.12)/[R]))/10.

FAQ

What is Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters?

The Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters formula is defined as the highest temperature at which the substance can exist as a liquid and is represented as T_real = ((p+(((a_PR*α)/((V_m^2)+(2*b_PR*V_m)-(b_PR^2)))))*((V_m-b_PR)/[R]))/T_r or Real Gas Temperature = ((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]))/Reduced Temperature. 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, α-function is a function of temperature and the acentric factor, 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 & Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.

How to calculate Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters?

The Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters formula is defined as the highest temperature at which the substance can exist as a liquid is calculated using Real Gas Temperature = ((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]))/Reduced Temperature. To calculate Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters, you need Pressure (p), Peng–Robinson Parameter a (a_PR), α-function (α), Molar Volume (V_m), Peng–Robinson Parameter b (b_PR) & Reduced Temperature (T_r). With our tool, you need to enter the respective value for Pressure, Peng–Robinson Parameter a, α-function, Molar Volume, Peng–Robinson Parameter b & 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 Real Gas Temperature?

In this formula, Real Gas Temperature uses Pressure, Peng–Robinson Parameter a, α-function, Molar Volume, Peng–Robinson Parameter b & Reduced Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -

Real Gas Temperature = Reduced Temperature*((Redlich–Kwong parameter b*Critical Pressure)/(0.08664*[R]))

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