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
Treal = ((p+(((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2)))))*((Vm-bPR)/[R]))/Tr
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
Treal = ((p+(((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2)))))*((Vm-bPR)/[R]))/Tr --> ((800+(((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2)))))*((22.4-0.12)/[R]))/10
Evaluating ... ...
Treal = 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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8 Critical Temperature Calculators

Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters
Go Critical 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]))/Reduced Temperature
Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters
Go 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
Critical Temperature given Peng Robinson Parameter a, and other Actual and Reduced Parameters
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
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
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
Go Critical Temperature = sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2)))
Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b
Go Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R])
Critical Temperature given Inversion Temperature
Go Critical Temperature = (4/27)*Inversion Temperature

20 Important Formulae on Different Models of Real Gas Calculators

Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters
Go 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
Temperature of Real Gas using Peng Robinson Equation
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 of Real Gas using Reduced Redlich Kwong Equation
Go Critical Pressure = Pressure/(((3*Reduced Temperature)/(Reduced Molar Volume-0.26))-(1/(0.26*sqrt(Temperature of Gas)*Reduced Molar Volume*(Reduced Molar Volume+0.26))))
Critical Temperature of Real Gas using Reduced Redlich Kwong Equation
Go Critical Temperature given RKE = Temperature of Gas/(((Reduced Pressure+(1/(0.26*Reduced Molar Volume*(Reduced Molar Volume+0.26))))*((Reduced Molar Volume-0.26)/3))^(2/3))
Actual Temperature of Real Gas using Reduced Redlich Kwong Equation
Go Temperature of Gas = Critical Temperature*(((Reduced Pressure+(1/(0.26*Reduced Molar Volume*(Reduced Molar Volume+0.26))))*((Reduced Molar Volume-0.26)/3))^(2/3))
Reduced Pressure given Peng Robinson Parameter b, other Actual and Reduced Parameters
Go Critical Pressure given PRP = Pressure/(0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b)
Reduced Temperature using Redlich Kwong Equation given of 'a' and 'b'
Go Temperature given PRP = Temperature of Gas/((3^(2/3))*(((2^(1/3))-1)^(4/3))*((Redlich–Kwong Parameter a/(Redlich–Kwong parameter b*[R]))^(2/3)))
Critical Pressure given Peng Robinson Parameter b and other Actual and Reduced Parameters
Go Critical Pressure given PRP = 0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b
Hamaker Coefficient
Go Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2
Actual Temperature given Peng Robinson parameter b, other reduced and critical parameters
Go Temperature given PRP = Reduced Temperature*((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))
Actual Temperature of Real Gas using Redlich Kwong Equation given 'b'
Go Real Gas Temperature = Reduced Temperature*((Redlich–Kwong parameter b*Critical Pressure)/(0.08664*[R]))
Reduced Temperature given Peng Robinson Parameter a, and other Actual and Critical Parameters
Go Temperature of Gas = Temperature/(sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2))))
Radius of Spherical Body 1 given Center-to-Center Distance
Go Radius of Spherical Body 1 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 2
Radius of Spherical Body 2 given Center-to-Center Distance
Go Radius of Spherical Body 2 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 1
Distance between Surfaces given Center-to-Center Distance
Go Distance Between Surfaces = Center-to-center Distance-Radius of Spherical Body 1-Radius of Spherical Body 2
Center-to-Center Distance
Go Center-to-center Distance = Radius of Spherical Body 1+Radius of Spherical Body 2+Distance Between Surfaces
Actual Pressure given Peng Robinson Parameter a, and other Reduced and Critical Parameters
Go Pressure given PRP = Reduced Pressure*(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)
Critical Temperature of Real Gas using Redlich Kwong Equation given 'b'
Go Critical Temperature given RKE and b = (Redlich–Kwong parameter b*Critical Pressure)/(0.08664*[R])
Redlich Kwong Parameter b at Critical Point
Go Parameter b = (0.08664*[R]*Critical Temperature)/Critical Pressure
Peng Robinson Parameter b of Real Gas given Critical Parameters
Go Parameter b = 0.07780*[R]*Critical Temperature/Critical Pressure

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

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
Treal = ((p+(((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2)))))*((Vm-bPR)/[R]))/Tr

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 Treal 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 (aPR), α-function (α), Molar Volume (Vm), Peng–Robinson Parameter b (bPR) & Reduced Temperature (Tr) 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 Treal = ((p+(((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2)))))*((Vm-bPR)/[R]))/Tr 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 (aPR), α-function (α), Molar Volume (Vm), Peng–Robinson Parameter b (bPR) & Reduced Temperature (Tr). 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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