Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters Calculator

✖Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.ⓘ Reduced Temperature [T_r]			+10% -10%
✖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.ⓘ Critical Temperature [T_c]			+10% -10%
✖Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.ⓘ Reduced Molar Volume [V_m,r]			+10% -10%
✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [V_m,c]			+10% -10%
✖Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter b [b_PR]			+10% -10%
✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter a [a_PR]			+10% -10%
✖α-function is a function of temperature and the acentric factor.ⓘ α-function [α]			+10% -10%
✖Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.ⓘ Reduced Pressure [P_r]			+10% -10%

✖Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters [P_c]

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Critical Pressure using Peng Robinson Equation given 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
P_c = ((([R]*(T_r*T_c))/((V_m,r*V_m,c)-b_PR))-((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2))))/P_r
This formula uses 1 Constants, 9 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
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.
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 - (Measured in Cubic Meter per Mole) - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure 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: 10 --> No Conversion Required
Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 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
Reduced Pressure: 3.675E-05 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_c = ((([R]*(T_r*T_c))/((V_m,r*V_m,c)-b_PR))-((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2))))/P_r --> ((([R]*(10*647))/((11.2*11.5)-0.12))-((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2))))/3.675E-05

Evaluating ... ...

P_c = 11375488.5485034

STEP 3: Convert Result to Output's Unit

11375488.5485034 Pascal --> No Conversion Required

FINAL ANSWER

11375488.5485034 ≈ 1.1E+7 Pascal <-- Critical Pressure

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Peng Robinson Model of Real Gas » Critical Pressure » Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters

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< Critical Pressure Calculators

Critical Pressure given Peng Robinson Parameter b and other Actual and Reduced Parameters

LaTeX Go Critical Pressure given PRP = 0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b

Critical Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters

LaTeX Go Critical Pressure = 0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a

Critical Pressure of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b

LaTeX Go Critical Pressure = 0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b

Critical Pressure of Real Gas using Peng Robinson Equation given Peng Robinson Parameter a

LaTeX Go Critical Pressure = 0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a

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

LaTeX Go

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 given Reduced and Critical Parameters?

Critical Pressure using Peng Robinson Equation given 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 given reduced and critical parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature. Critical Pressure is denoted by P_c symbol.

How to calculate Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters, enter Reduced Temperature (T_r), Critical Temperature (T_c), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Peng–Robinson Parameter b (b_PR), Peng–Robinson Parameter a (a_PR), α-function (α) & Reduced Pressure (P_r) and hit the calculate button. Here is how the Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 1.1E+7 = ((([R]*(10*647))/((11.2*11.5)-0.12))-((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2))))/3.675E-05.

FAQ

What is Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters?

The Critical Pressure using Peng Robinson equation given reduced and critical parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature and is represented as P_c = ((([R]*(T_r*T_c))/((V_m,r*V_m,c)-b_PR))-((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2))))/P_r 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 & 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 given Reduced and Critical Parameters?

The Critical Pressure using Peng Robinson equation given 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 given Reduced and Critical Parameters, you need Reduced Temperature (T_r), Critical Temperature (T_c), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Peng–Robinson Parameter b (b_PR), Peng–Robinson Parameter a (a_PR), α-function (α) & Reduced Pressure (P_r). 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 & 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 & Reduced Pressure. We can use 3 other way(s) to calculate the same, which is/are as follows -

Critical Pressure = 0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a
Critical Pressure = 0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a
Critical Pressure = 0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b

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