Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical Molar Volume = ((([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/(Reduced Temperature*Critical Temperature For Clausius Model))))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas
Vm,c = ((([R]*(Tr*T'c))/((Pr*P'c)+(a/(Tr*T'c))))+b')/V'm,r
This formula uses 1 Constants, 8 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
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.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
Critical Temperature For Clausius Model - (Measured in Kelvin) - Critical Temperature For Clausius Model is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, 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 of Real Gas - (Measured in Pascal) - Critical Pressure of Real Gas is the minimum pressure required to liquify a substance at the critical temperature.
Clausius Parameter a - Clausius parameter a is an empirical parameter characteristic to equation obtained from Clausius model of real gas.
Clausius Parameter b for Real Gas - Clausius Parameter b for Real Gas is an empirical parameter characteristic to equation obtained from Clausius model of real gas.
Reduced Molar Volume for Real Gas - Reduced Molar Volume for Real Gas of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.
STEP 1: Convert Input(s) to Base Unit
Reduced Temperature: 10 --> No Conversion Required
Critical Temperature For Clausius Model: 154.4 Kelvin --> 154.4 Kelvin No Conversion Required
Reduced Pressure: 0.8 --> No Conversion Required
Critical Pressure of Real Gas: 4600000 Pascal --> 4600000 Pascal No Conversion Required
Clausius Parameter a: 0.1 --> No Conversion Required
Clausius Parameter b for Real Gas: 0.00243 --> No Conversion Required
Reduced Molar Volume for Real Gas: 8.96 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vm,c = ((([R]*(Tr*T'c))/((Pr*P'c)+(a/(Tr*T'c))))+b')/V'm,r --> ((([R]*(10*154.4))/((0.8*4600000)+(0.1/(10*154.4))))+0.00243)/8.96
Evaluating ... ...
Vm,c = 0.000660542334354458
STEP 3: Convert Result to Output's Unit
0.000660542334354458 Cubic Meter per Mole --> No Conversion Required
FINAL ANSWER
0.000660542334354458 0.000661 Cubic Meter per Mole <-- Critical Molar Volume
(Calculation completed in 00.004 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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K J Somaiya College of science (K J Somaiya), Mumbai
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3 Critical Molar Volume Calculators

Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters
Go Critical Molar Volume = ((([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/(Reduced Temperature*Critical Temperature For Clausius Model))))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas
Critical Molar Volume of Real Gas using Clausius Equation given Reduced and Actual Parameters
Go Critical Molar Volume given RP = ((([R]*Temperature of Real Gas)/(Pressure+(Clausius Parameter a/Temperature of Real Gas)))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas
Critical Molar Volume using Clausius Equation given Actual and Critical Parameters
Go Critical Molar Volume given RP = ((([R]*Temperature of Real Gas)/(Pressure+(Clausius Parameter a/Temperature of Real Gas)))+Clausius Parameter b for Real Gas)/Molar Volume

Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters Formula

Critical Molar Volume = ((([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/(Reduced Temperature*Critical Temperature For Clausius Model))))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas
Vm,c = ((([R]*(Tr*T'c))/((Pr*P'c)+(a/(Tr*T'c))))+b')/V'm,r

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 Molar Volume using Clausius Equation given Reduced and Critical Parameters?

Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters calculator uses Critical Molar Volume = ((([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/(Reduced Temperature*Critical Temperature For Clausius Model))))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas to calculate the Critical Molar Volume, The Critical Molar Volume using Clausius equation given reduced and critical parameters formula is defined as the volume occupied by gas at critical temperature and pressure per mole. Critical Molar Volume is denoted by Vm,c symbol.

How to calculate Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters, enter Reduced Temperature (Tr), Critical Temperature For Clausius Model (T'c), Reduced Pressure (Pr), Critical Pressure of Real Gas (P'c), Clausius Parameter a (a), Clausius Parameter b for Real Gas (b') & Reduced Molar Volume for Real Gas (V'm,r) and hit the calculate button. Here is how the Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 0.000528 = ((([R]*(10*154.4))/((0.8*4600000)+(0.1/(10*154.4))))+0.00243)/8.96.

FAQ

What is Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters?
The Critical Molar Volume using Clausius equation given reduced and critical parameters formula is defined as the volume occupied by gas at critical temperature and pressure per mole and is represented as Vm,c = ((([R]*(Tr*T'c))/((Pr*P'c)+(a/(Tr*T'c))))+b')/V'm,r or Critical Molar Volume = ((([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/(Reduced Temperature*Critical Temperature For Clausius Model))))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas. Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless, Critical Temperature For Clausius Model is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, the substance can exist both as a liquid and vapor, Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless, Critical Pressure of Real Gas is the minimum pressure required to liquify a substance at the critical temperature, Clausius parameter a is an empirical parameter characteristic to equation obtained from Clausius model of real gas, Clausius Parameter b for Real Gas is an empirical parameter characteristic to equation obtained from Clausius model of real gas & Reduced Molar Volume for Real Gas of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.
How to calculate Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters?
The Critical Molar Volume using Clausius equation given reduced and critical parameters formula is defined as the volume occupied by gas at critical temperature and pressure per mole is calculated using Critical Molar Volume = ((([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/(Reduced Temperature*Critical Temperature For Clausius Model))))+Clausius Parameter b for Real Gas)/Reduced Molar Volume for Real Gas. To calculate Critical Molar Volume using Clausius Equation given Reduced and Critical Parameters, you need Reduced Temperature (Tr), Critical Temperature For Clausius Model (T'c), Reduced Pressure (Pr), Critical Pressure of Real Gas (P'c), Clausius Parameter a (a), Clausius Parameter b for Real Gas (b') & Reduced Molar Volume for Real Gas (V'm,r). With our tool, you need to enter the respective value for Reduced Temperature, Critical Temperature For Clausius Model, Reduced Pressure, Critical Pressure of Real Gas, Clausius Parameter a, Clausius Parameter b for Real Gas & Reduced Molar Volume for Real Gas and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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