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Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter Solution

STEP 0: Pre-Calculation Summary
Formula Used
critical_temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)
Tc = T/((1-((sqrt(α)-1)/k))^2)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Temperature - Temperature is the degree or intensity of heat present in a substance or object. (Measured in Kelvin)
α-function- α-function is a function of temperature and the acentric factor.
Pure Component Parameter- Pure Component Parameter is a function of the acentric factor.
STEP 1: Convert Input(s) to Base Unit
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
α-function: 2 --> No Conversion Required
Pure Component Parameter: 1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tc = T/((1-((sqrt(α)-1)/k))^2) --> 85/((1-((sqrt(2)-1)/1))^2)
Evaluating ... ...
Tc = 247.708152801713
STEP 3: Convert Result to Output's Unit
247.708152801713 Kelvin --> No Conversion Required
FINAL ANSWER
247.708152801713 Kelvin <-- Critical Temperature
(Calculation completed in 00.016 seconds)

10+ Peng–Robinson model of Real Gas Calculators

Peng–Robinson α-function using Peng–Robinson equation in terms of reduced and critical parameters
alpha_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 Go
Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters
critical_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))))/Reduced Pressure Go
Peng–Robinson parameter a using Peng–Robinson equation in terms of reduced and critical parameters
peng_robinson_parameter_a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))/α-function Go
Pressure of real gas using Peng–Robinson equation in terms of reduced and critical parameters
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))) Go
Temperature of real gas using Peng–Robinson equation in terms of reduced and critical parameters
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]) Go
Critical Pressure of real gas using Peng–Robinson equation in terms of reduced and actual parameters
critical_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))))/Reduced Pressure Go
Peng–Robinson α-function using Peng–Robinson equation
alpha_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 Go
Temperature of real gas using Peng–Robinson equation
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]) Go
Pressure of real gas using Peng–Robinson equation
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))) Go
Peng–Robinson parameter a using Peng–Robinson equation
peng_robinson_parameter_a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/α-function Go

Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter Formula

critical_temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)
Tc = T/((1-((sqrt(α)-1)/k))^2)

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 for Peng–Robinson equation using alpha-function and pure component parameter?

Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter calculator uses critical_temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2) to calculate the Critical Temperature, The Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter formula is defined as the highest temperature at which the substance can exist as a liquid. Critical Temperature and is denoted by Tc symbol.

How to calculate Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter using this online calculator? To use this online calculator for Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter, enter Temperature (T), α-function (α) and Pure Component Parameter (k) and hit the calculate button. Here is how the Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter calculation can be explained with given input values -> 247.7082 = 85/((1-((sqrt(2)-1)/1))^2).

FAQ

What is Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter?
The Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter formula is defined as the highest temperature at which the substance can exist as a liquid and is represented as Tc = T/((1-((sqrt(α)-1)/k))^2) or critical_temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2). Temperature is the degree or intensity of heat present in a substance or object, α-function is a function of temperature and the acentric factor and Pure Component Parameter is a function of the acentric factor.
How to calculate Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter?
The Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter formula is defined as the highest temperature at which the substance can exist as a liquid is calculated using critical_temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2). To calculate Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter, you need Temperature (T), α-function (α) and Pure Component Parameter (k). With our tool, you need to enter the respective value for Temperature, α-function and Pure Component Parameter 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 Temperature, α-function and Pure Component Parameter. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • 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)))
  • 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 = (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])
  • 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])
  • peng_robinson_parameter_a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/α-function
  • peng_robinson_parameter_a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))/α-function
  • alpha_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
  • alpha_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_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))))/Reduced Pressure
  • critical_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))))/Reduced Pressure
Where is the Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter calculator used?
Among many, Critical Temperature for Peng–Robinson equation using alpha-function and pure component parameter calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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