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

STEP 0: Pre-Calculation Summary
Formula Used
Reduced 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))))/Critical Pressure
Pr = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pc
This formula uses 1 Constants, 7 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
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.
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.
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
Temperature: 85 Kelvin --> 85 Kelvin 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
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
α-function: 2 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pr = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pc --> ((([R]*85)/(22.4-0.12))-((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2))))/218
Evaluating ... ...
Pr = 0.14550436802988
STEP 3: Convert Result to Output's Unit
0.14550436802988 --> No Conversion Required
FINAL ANSWER
0.14550436802988 0.145504 <-- Reduced Pressure
(Calculation completed in 00.004 seconds)

Credits

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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6 Reduced Pressure Calculators

Reduced Pressure using Peng Robinson Equation given Reduced and Critical Parameters
Go Reduced Pressure = ((([R]*(Reduced Temperature*Critical Temperature of Real Gas))/((Reduced Molar Volume for P-R Method*Critical Molar Volume for Peng Robinson Model)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume for P-R Method*Critical Molar Volume for Peng Robinson Model)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume for P-R Method*Critical Molar Volume for Peng Robinson Model))-(Peng–Robinson Parameter b^2))))/Critical Pressure for Peng Robinson Model
Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters
Go Reduced 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))))/Critical Pressure
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 Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters
Go Reduced Pressure = Pressure/(0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a)
Reduced Pressure given Peng Robinson Parameter b, other Actual and Critical Parameters
Go Reduced Pressure = Pressure/(0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b)
Reduced Pressure given Peng Robinson Parameter a, and other Actual and Critical Parameters
Go Reduced Pressure = Pressure/(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)

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

Reduced 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))))/Critical Pressure
Pr = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pc

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

Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters calculator uses Reduced 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))))/Critical Pressure to calculate the Reduced Pressure, The Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters formula is defined as the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless. Reduced Pressure is denoted by Pr symbol.

How to calculate Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters using this online calculator? To use this online calculator for Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters, enter Temperature (T), Molar Volume (Vm), Peng–Robinson Parameter b (bPR), Peng–Robinson Parameter a (aPR), α-function (α) & Critical Pressure (Pc) and hit the calculate button. Here is how the Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters calculation can be explained with given input values -> 0.146029 = ((([R]*85)/(22.4-0.12))-((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2))))/218.

FAQ

What is Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters?
The Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters formula is defined as the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless and is represented as Pr = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pc or Reduced 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))))/Critical Pressure. Temperature is the degree or intensity of heat present in a substance or object, 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, 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 & Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
How to calculate Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters?
The Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters formula is defined as the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless is calculated using Reduced 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))))/Critical Pressure. To calculate Reduced Pressure using Peng Robinson Equation given Critical and Actual Parameters, you need Temperature (T), Molar Volume (Vm), Peng–Robinson Parameter b (bPR), Peng–Robinson Parameter a (aPR), α-function (α) & Critical Pressure (Pc). With our tool, you need to enter the respective value for Temperature, Molar Volume, Peng–Robinson Parameter b, Peng–Robinson Parameter a, α-function & 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 Reduced Pressure?
In this formula, Reduced Pressure uses Temperature, Molar Volume, Peng–Robinson Parameter b, Peng–Robinson Parameter a, α-function & Critical Pressure. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Reduced Pressure = Pressure/(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)
  • Reduced Pressure = Pressure/(0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a)
  • Reduced Pressure = Pressure/(0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b)
  • Reduced Pressure = ((([R]*(Reduced Temperature*Critical Temperature of Real Gas))/((Reduced Molar Volume for P-R Method*Critical Molar Volume for Peng Robinson Model)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume for P-R Method*Critical Molar Volume for Peng Robinson Model)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume for P-R Method*Critical Molar Volume for Peng Robinson Model))-(Peng–Robinson Parameter b^2))))/Critical Pressure for Peng Robinson Model
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