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Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
Pc = ((([R]*(Tr*Tc))/((Vm,r*Vm,c)-b))-((a*α)/(((Vm,r*Vm,c)^2)+(2*b*(Vm,r*Vm,c))-(b^2))))/Pr
This formula uses 1 Constants, 8 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Reduced Temperature- Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
Critical Temperature - 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. (Measured in Kelvin)
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.
Critical Molar Volume - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole. (Measured in Cubic Meter 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.
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.
Reduced Pressure- Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
STEP 1: Convert Input(s) to Base Unit
Reduced Temperature: 0.131376 --> No Conversion Required
Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
Reduced Molar Volume: 10 --> No Conversion Required
Critical Molar Volume: 10 Cubic Meter per Mole --> 10 Cubic Meter per Mole No Conversion Required
Peng–Robinson parameter b: 0.1 --> No Conversion Required
Peng–Robinson parameter a: 0.1 --> No Conversion Required
α-function: 2 --> No Conversion Required
Reduced Pressure: 3.67E-05 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pc = ((([R]*(Tr*Tc))/((Vm,r*Vm,c)-b))-((a*α)/(((Vm,r*Vm,c)^2)+(2*b*(Vm,r*Vm,c))-(b^2))))/Pr --> ((([R]*(0.131376*647))/((10*10)-0.1))-((0.1*2)/(((10*10)^2)+(2*0.1*(10*10))-(0.1^2))))/3.67E-05
Evaluating ... ...
Pc = 192762.132722066
STEP 3: Convert Result to Output's Unit
192762.132722066 Pascal --> No Conversion Required
FINAL ANSWER
192762.132722066 Pascal <-- Critical Pressure
(Calculation completed in 00.015 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 Pressure using Peng–Robinson equation in terms of reduced and critical parameters Formula

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
Pc = ((([R]*(Tr*Tc))/((Vm,r*Vm,c)-b))-((a*α)/(((Vm,r*Vm,c)^2)+(2*b*(Vm,r*Vm,c))-(b^2))))/Pr

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 Pressure using Peng–Robinson equation in terms of reduced and critical parameters?

Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters calculator uses 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 to calculate the Critical Pressure, The Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature. Critical Pressure and is denoted by Pc symbol.

How to calculate Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters using this online calculator? To use this online calculator for Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters, enter Reduced Temperature (Tr), Critical Temperature (Tc), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c), Peng–Robinson parameter b (b), Peng–Robinson parameter a (a), α-function (α) and Reduced Pressure (Pr) and hit the calculate button. Here is how the Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters calculation can be explained with given input values -> 192762.1 = ((([R]*(0.131376*647))/((10*10)-0.1))-((0.1*2)/(((10*10)^2)+(2*0.1*(10*10))-(0.1^2))))/3.67E-05.

FAQ

What is Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters?
The Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature and is represented as Pc = ((([R]*(Tr*Tc))/((Vm,r*Vm,c)-b))-((a*α)/(((Vm,r*Vm,c)^2)+(2*b*(Vm,r*Vm,c))-(b^2))))/Pr or 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. Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless, 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 Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, 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 and Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
How to calculate Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters?
The Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature is calculated using 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. To calculate Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters, you need Reduced Temperature (Tr), Critical Temperature (Tc), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c), Peng–Robinson parameter b (b), Peng–Robinson parameter a (a), α-function (α) and Reduced Pressure (Pr). With our tool, you need to enter the respective value for Reduced Temperature, Critical Temperature, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson parameter b, Peng–Robinson parameter a, α-function and Reduced 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 Pressure?
In this formula, Critical Pressure uses Reduced Temperature, Critical Temperature, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson parameter b, Peng–Robinson parameter a, α-function and Reduced Pressure. 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 Pressure using Peng–Robinson equation in terms of reduced and critical parameters calculator used?
Among many, Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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