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Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Formula

GoClausius Parameter b given Critical Parameters Formula

GoClausius Parameter b given Pressure, Temperature and Molar Volume of Real Gas Formula

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Clausius parameter b is an empirical parameter characteristic to equation obtained from Clausius model of real gas. Check FAQs

b = (V m,r \cdot V m,c) - (\frac{[R] \cdot (T r \cdot T c)}{(P r \cdot P c) + (\frac{a}{(T r \cdot T c) \cdot ({((V m,r \cdot V m,c) + c)}^{2})})})

b - Clausius Parameter b?V_m,r - Reduced Molar Volume?V_m,c - Critical Molar Volume?T_r - Reduced Temperature?T_c - Critical Temperature?P_r - Reduced Pressure?P_c - Critical Pressure?a - Clausius Parameter a?c - Clausius Parameter c?[R] - Universal gas constant?

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Example

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Here is how the Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation equation looks like with Values.

Here is how the Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation equation looks like with Units.

Here is how the Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation equation looks like.

-179.6551 = (11.2 \cdot 11.5) - (\frac{8.3145 \cdot (10 \cdot 647)}{(0.8 \cdot 218) + (\frac{0.1}{(10 \cdot 647) \cdot ({((11.2 \cdot 11.5) + 0.0002)}^{2})})})

-179.6551 = (11.2 \cdot 11.5m³/mol) - (\frac{8.3145 \cdot (10 \cdot 647K)}{(0.8 \cdot 218Pa) + (\frac{0.1}{(10 \cdot 647K) \cdot ({((11.2 \cdot 11.5m³/mol) + 0.0002)}^{2})})})

-179.6551 = (11.2 \cdot 11.5) - (\frac{8.3145 \cdot (10 \cdot 647)}{(0.8 \cdot 218) + (\frac{0.1}{(10 \cdot 647) \cdot ({((11.2 \cdot 11.5) + 0.0002)}^{2})})})

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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Solution

Follow our step by step solution on how to calculate Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation?

FIRST Step Consider the formula

b = (V m,r \cdot V m,c) - (\frac{[R] \cdot (T r \cdot T c)}{(P r \cdot P c) + (\frac{a}{(T r \cdot T c) \cdot ({((V m,r \cdot V m,c) + c)}^{2})})})

Next Step Substitute values of Variables

∴

b = (11.2 \cdot 11.5m³/mol) - (\frac{[R] \cdot (10 \cdot 647K)}{(0.8 \cdot 218Pa) + (\frac{0.1}{(10 \cdot 647K) \cdot ({((11.2 \cdot 11.5m³/mol) + 0.0002)}^{2})})})

Next Step Substitute values of Constants

∴

b = (11.2 \cdot 11.5m³/mol) - (\frac{8.3145 \cdot (10 \cdot 647K)}{(0.8 \cdot 218Pa) + (\frac{0.1}{(10 \cdot 647K) \cdot ({((11.2 \cdot 11.5m³/mol) + 0.0002)}^{2})})})

Next Step Prepare to Evaluate

∴

b = (11.2 \cdot 11.5) - (\frac{8.3145 \cdot (10 \cdot 647)}{(0.8 \cdot 218) + (\frac{0.1}{(10 \cdot 647) \cdot ({((11.2 \cdot 11.5) + 0.0002)}^{2})})})

Next Step Evaluate

∴

b = -179.655121210803

LAST Step Rounding Answer

∴

b = -179.6551

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Formula Elements

Variables

Constants

Clausius Parameter b

Clausius parameter b is an empirical parameter characteristic to equation obtained from Clausius model of real gas.

Symbol: b

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

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.

Symbol: V_m,r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Critical Molar Volume

Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.

Symbol: V_m,c

Measurement: Molar Magnetic SusceptibilityUnit: m³/mol

Note: Value can be positive or negative.

Reduced Temperature

Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.

Symbol: T_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Critical Temperature

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.

Symbol: T_c

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Reduced Pressure

Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.

Symbol: P_r

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Critical Pressure

Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.

Symbol: P_c

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Clausius Parameter a

Clausius parameter a is an empirical parameter characteristic to equation obtained from Clausius model of real gas.

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Clausius Parameter c

Clausius parameter c is an empirical parameter characteristic to equation obtained from Clausius model of real gas.

Symbol: c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

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Created by Prerana Bakli

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

Prerana Bakli has created this Formula and 800+ more formulas!

Verified by Prashant Singh

K J Somaiya College of science (K J Somaiya), Mumbai

Prashant Singh has verified this Formula and 500+ more formulas!

Other Formulas to find Clausius Parameter b

Go Clausius Parameter b given Critical Parameters

b = V c - (\frac{[R] \cdot T c}{4 \cdot P' c})

Go Clausius Parameter b given Pressure, Temperature and Molar Volume of Real Gas

b = V m - (\frac{[R] \cdot T rg}{p + (\frac{a}{T rg \cdot ({(V m + c)}^{2})})})

Other formulas in Clausius Parameter category

Go Clausius Parameter given Critical Parameters

a = \frac{27 \cdot ({[R]}^{2}) \cdot ({T c}^{3})}{64 \cdot P c}

Go Clausius Parameter given Pressure, Temperature and Molar Volume of Real Gas

a = ((\frac{[R] \cdot T rg}{V m - b}) - p) \cdot (T rg \cdot ({(V m + c)}^{2}))

How to Evaluate Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation?

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation evaluator uses Clausius Parameter b = (Reduced Molar Volume*Critical Molar Volume)-(([R]*(Reduced Temperature*Critical Temperature))/((Reduced Pressure*Critical Pressure)+(Clausius Parameter a/((Reduced Temperature*Critical Temperature)*(((Reduced Molar Volume*Critical Molar Volume)+Clausius Parameter c)^2))))) to evaluate the Clausius Parameter b, The Clausius parameter b given reduced and critical parameters using Clausius equation formula is defined as an empirical parameter characteristic to equation obtained from Clausius model of real gas. Clausius Parameter b is denoted by b symbol.

How to evaluate Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation using this online evaluator? To use this online evaluator for Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation, enter Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Reduced Temperature (T_r), Critical Temperature (T_c), Reduced Pressure (P_r), Critical Pressure (P_c), Clausius Parameter a (a) & Clausius Parameter c (c) and hit the calculate button.

FAQs on Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation

What is the formula to find Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation?

The formula of Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation is expressed as Clausius Parameter b = (Reduced Molar Volume*Critical Molar Volume)-(([R]*(Reduced Temperature*Critical Temperature))/((Reduced Pressure*Critical Pressure)+(Clausius Parameter a/((Reduced Temperature*Critical Temperature)*(((Reduced Molar Volume*Critical Molar Volume)+Clausius Parameter c)^2))))). Here is an example- -179.655121 = (11.2*11.5)-(([R]*(10*647))/((0.8*218)+(0.1/((10*647)*(((11.2*11.5)+0.0002)^2))))).

How to calculate Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation?

With Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Reduced Temperature (T_r), Critical Temperature (T_c), Reduced Pressure (P_r), Critical Pressure (P_c), Clausius Parameter a (a) & Clausius Parameter c (c) we can find Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation using the formula - Clausius Parameter b = (Reduced Molar Volume*Critical Molar Volume)-(([R]*(Reduced Temperature*Critical Temperature))/((Reduced Pressure*Critical Pressure)+(Clausius Parameter a/((Reduced Temperature*Critical Temperature)*(((Reduced Molar Volume*Critical Molar Volume)+Clausius Parameter c)^2))))). This formula also uses Universal gas constant .

What are the other ways to Calculate Clausius Parameter b?

Here are the different ways to Calculate Clausius Parameter b-

Clausius Parameter b=Critical Volume-(([R]*Critical Temperature)/(4*Critical Pressure of Real Gas))
Clausius Parameter b=Molar Volume-(([R]*Temperature of Real Gas)/(Pressure+(Clausius Parameter a/(Temperature of Real Gas*((Molar Volume+Clausius Parameter c)^2)))))

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Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Formula

​GoClausius Parameter b given Critical Parameters Formula

​GoClausius Parameter b given Pressure, Temperature and Molar Volume of Real Gas Formula

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Example

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Solution

Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation Formula Elements

Credits

Other Formulas to find Clausius Parameter b

Other formulas in Clausius Parameter category

How to Evaluate Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation?

FAQs on Clausius Parameter b given Reduced and Critical Parameters using Clausius Equation

Variable Name

GoClausius Parameter b given Critical Parameters Formula

GoClausius Parameter b given Pressure, Temperature and Molar Volume of Real Gas Formula