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

✖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 [P_c]			+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 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%
✖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 using Peng Robinson Equation given Reduced and Critical Parameters [T_c]

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Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
T_c = (((P_r*P_c)+(((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2)))))*(((V_m,r*V_m,c)-b_PR)/[R]))/T_r
This formula uses 1 Constants, 9 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.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
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 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.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.

STEP 1: Convert Input(s) to Base Unit

Reduced Pressure: 3.675E-05 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
α-function: 2 --> 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
Reduced Temperature: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_c = (((P_r*P_c)+(((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2)))))*(((V_m,r*V_m,c)-b_PR)/[R]))/T_r --> (((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R]))/10

Evaluating ... ...

T_c = 0.0124177392063826

STEP 3: Convert Result to Output's Unit

0.0124177392063826 Kelvin --> No Conversion Required

FINAL ANSWER

0.0124177392063826 ≈ 0.012418 Kelvin <-- Critical Temperature

(Calculation completed in 00.020 seconds)

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

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< Critical Temperature Calculators

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

LaTeX 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

LaTeX 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

LaTeX 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

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

Critical Temperature 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 Temperature using Peng Robinson Equation given Reduced and Critical Parameters?

Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters calculator uses 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 to calculate the Critical Temperature, The Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the highest temperature at which the substance can exist as a liquid. Critical Temperature is denoted by T_c symbol.

How to calculate Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters, enter Reduced Pressure (P_r), Critical Pressure (P_c), Peng–Robinson Parameter a (a_PR), α-function (α), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Peng–Robinson Parameter b (b_PR) & Reduced Temperature (T_r) and hit the calculate button. Here is how the Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 0.01241 = (((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R]))/10.

FAQ

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

The Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the highest temperature at which the substance can exist as a liquid and is represented as T_c = (((P_r*P_c)+(((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2)))))*(((V_m,r*V_m,c)-b_PR)/[R]))/T_r or 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. Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature, 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 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 & Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.

How to calculate Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters?

The Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the highest temperature at which the substance can exist as a liquid is calculated using 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. To calculate Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters, you need Reduced Pressure (P_r), Critical Pressure (P_c), Peng–Robinson Parameter a (a_PR), α-function (α), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Peng–Robinson Parameter b (b_PR) & Reduced Temperature (T_r). With our tool, you need to enter the respective value for Reduced Pressure, Critical Pressure, Peng–Robinson Parameter a, α-function, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson Parameter b & Reduced Temperature 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 Reduced Pressure, Critical Pressure, Peng–Robinson Parameter a, α-function, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson Parameter b & Reduced Temperature. We can use 3 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])

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