Reduced Molar Volume of Real Gas using Clausius 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 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.ⓘ Critical Temperature For Clausius Model [T'_c]			+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 of Real Gas is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure of Real Gas [P'_c]			+10% -10%
✖Clausius parameter a is an empirical parameter characteristic to equation obtained from Clausius model of real gas.ⓘ Clausius Parameter a [a]			+10% -10%
✖Clausius Parameter b for Real Gas is an empirical parameter characteristic to equation obtained from Clausius model of real gas.ⓘ Clausius Parameter b for Real Gas [b']			+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%

✖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.ⓘ Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters [V'_m,r]

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Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reduced Molar Volume for Real Gas = ((([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)/Critical Molar Volume
V'_m,r = ((([R]*(T_r*T'_c))/((P_r*P'_c)+(a/(T_r*T'_c))))+b')/V_m,c
This formula uses 1 Constants, 8 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

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.
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.
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.

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
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V'_m,r = ((([R]*(T_r*T'_c))/((P_r*P'_c)+(a/(T_r*T'_c))))+b')/V_m,c --> ((([R]*(10*154.4))/((0.8*4600000)+(0.1/(10*154.4))))+0.00243)/11.5

Evaluating ... ...

V'_m,r = 0.000514648636157908

STEP 3: Convert Result to Output's Unit

0.000514648636157908 --> No Conversion Required

FINAL ANSWER

0.000514648636157908 ≈ 0.000515 <-- Reduced Molar Volume for Real Gas

(Calculation completed in 00.004 seconds)

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Reduced Volume Calculators

Reduced Volume of Real Gas given Clausius Parameter c, Reduced and Actual Parameters

LaTeX Go Reduced Volume given RP AP = Volume of Real Gas/(((3*[R]*(Real Gas Temperature/Reduced Temperature))/(8*(Real Gas Pressure/Reduced Pressure)))-Clausius Parameter c)

Reduced Volume of Real Gas given Clausius Parameter b, Reduced and Actual Parameters

LaTeX Go Reduced Volume = Volume of Real Gas/(Clausius Parameter b for Real Gas+(([R]*(Temperature of Real Gas/Reduced Temperature))/(4*(Pressure/Reduced Pressure))))

Reduced Volume of Real Gas given Clausius Parameter b and Actual Parameters

LaTeX Go Reduced Volume = Volume of Real Gas/(Clausius Parameter b for Real Gas+(([R]*Critical Temperature For Clausius Model)/(4*Critical Pressure of Real Gas)))

Reduced Volume of Real Gas given Clausius Parameter c and Actual Parameters

LaTeX Go Reduced Volume = Volume of Real Gas/(((3*[R]*Critical Temperature)/(8*Critical Pressure of Real Gas))-Clausius Parameter c)

Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters Formula

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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 Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters?

Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters calculator uses Reduced Molar Volume for Real Gas = ((([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)/Critical Molar Volume to calculate the Reduced Molar Volume for Real Gas, The Reduced Molar Volume of real gas using Clausius equation given reduced and critical parameters formula of a fluid is computed from the ideal gas law as the ratio of its actual volume to critical volume per mole. Reduced Molar Volume for Real Gas is denoted by V'_m,r symbol.

How to calculate Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters, enter Reduced Temperature (T_r), Critical Temperature For Clausius Model (T'_c), Reduced Pressure (P_r), Critical Pressure of Real Gas (P'_c), Clausius Parameter a (a), Clausius Parameter b for Real Gas (b') & Critical Molar Volume (V_m,c) and hit the calculate button. Here is how the Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 0.000515 = ((([R]*(10*154.4))/((0.8*4600000)+(0.1/(10*154.4))))+0.00243)/11.5.

FAQ

What is Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters?

The Reduced Molar Volume of real gas using Clausius equation given reduced and critical parameters formula of a fluid is computed from the ideal gas law as the ratio of its actual volume to critical volume per mole and is represented as V'_m,r = ((([R]*(T_r*T'_c))/((P_r*P'_c)+(a/(T_r*T'_c))))+b')/V_m,c or Reduced Molar Volume for Real Gas = ((([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)/Critical Molar Volume. 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 & Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.

How to calculate Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters?

The Reduced Molar Volume of real gas using Clausius equation given reduced and critical parameters formula of a fluid is computed from the ideal gas law as the ratio of its actual volume to critical volume per mole is calculated using Reduced Molar Volume for Real Gas = ((([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)/Critical Molar Volume. To calculate Reduced Molar Volume of Real Gas using Clausius Equation given Reduced and Critical Parameters, you need Reduced Temperature (T_r), Critical Temperature For Clausius Model (T'_c), Reduced Pressure (P_r), Critical Pressure of Real Gas (P'_c), Clausius Parameter a (a), Clausius Parameter b for Real Gas (b') & Critical Molar Volume (V_m,c). 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 & Critical Molar Volume 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 Molar Volume for Real Gas?

In this formula, Reduced Molar Volume for Real Gas uses Reduced Temperature, Critical Temperature For Clausius Model, Reduced Pressure, Critical Pressure of Real Gas, Clausius Parameter a, Clausius Parameter b for Real Gas & Critical Molar Volume. We can use 2 other way(s) to calculate the same, which is/are as follows -

Reduced Molar Volume for Real Gas = ((([R]*Temperature of Real Gas)/(Pressure+(Clausius Parameter a/Temperature of Real Gas)))+Clausius Parameter b for Real Gas)/Critical Molar Volume
Reduced Molar Volume for Real Gas = ((([R]*Temperature of Real Gas)/(Pressure+(Clausius Parameter a/Temperature of Real Gas)))+Clausius Parameter b for Real Gas)/Molar Volume

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