Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R])
Tc = (bPR*Pc)/(0.07780*[R])
This formula uses 1 Constants, 3 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tc = (bPR*Pc)/(0.07780*[R]) --> (0.12*218)/(0.07780*[R])
Evaluating ... ...
Tc = 40.4411929038267
STEP 3: Convert Result to Output's Unit
40.4411929038267 Kelvin --> No Conversion Required
FINAL ANSWER
40.4411929038267 40.44119 Kelvin <-- Critical Temperature
(Calculation completed in 00.004 seconds)

Credits

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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K J Somaiya College of science (K J Somaiya), Mumbai
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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

Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b Formula

Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R])
Tc = (bPR*Pc)/(0.07780*[R])

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 of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b?

Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b calculator uses Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]) to calculate the Critical Temperature, The Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b formula is defined as the highest temperature at which the substance can exist as a liquid. Critical Temperature is denoted by Tc symbol.

How to calculate Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b using this online calculator? To use this online calculator for Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b, enter Peng–Robinson Parameter b (bPR) & Critical Pressure (Pc) and hit the calculate button. Here is how the Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b calculation can be explained with given input values -> 67.40199 = (0.12*218)/(0.07780*[R]).

FAQ

What is Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b?
The Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b formula is defined as the highest temperature at which the substance can exist as a liquid and is represented as Tc = (bPR*Pc)/(0.07780*[R]) or Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]). 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.
How to calculate Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b?
The Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b formula is defined as the highest temperature at which the substance can exist as a liquid is calculated using Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]). To calculate Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b, you need Peng–Robinson Parameter b (bPR) & Critical Pressure (Pc). With our tool, you need to enter the respective value for Peng–Robinson Parameter b & Critical Pressure 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 Critical Temperature?
In this formula, Critical Temperature uses Peng–Robinson Parameter b & Critical Pressure. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)
  • Critical Temperature = sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2)))
  • Critical Temperature = (Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R])
  • Critical Temperature = sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2)))
  • 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 = (4/27)*Inversion Temperature
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