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Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters Calculator

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✖Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.ⓘ Reduced Pressure [Pr]
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-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%
✖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 for Real Gas [V'm,r]
+10%
-10%
✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [Vm,c]
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-10%
✖Clausius parameter c is an empirical parameter characteristic to equation obtained from Clausius model of real gas.ⓘ Clausius Parameter c [c]
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-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']
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-10%
✖Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.ⓘ Reduced Temperature [Tr]
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✖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 of Real Gas using Clausius Equation given Reduced and Critical Parameters [T'c]
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Formula
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Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters

Formula
`"T'"_{"c"} = ((("P"_{"r"}*"P'"_{"c"})+("a"/(((("V'"_{"m,r"}*"V"_{"m,c"})+"c")^2))))*((("V'"_{"m,r"}*"V"_{"m,c"})-"b'")/"[R]"))/"T"_{"r"}`

Example
`"4.6E^6K"=((("0.8"*"4.6E^6Pa")+("0.1"/(((("8.96"*"11.5m³/mol")+"0.0002")^2))))*((("8.96"*"11.5m³/mol")-"2.43E^-3")/"[R]"))/"10"`

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

STEP 0: Pre-Calculation Summary
Formula Used
Critical Temperature For Clausius Model = (((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/((((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2))))*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature
T'c = (((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R]))/Tr
This formula uses 1 Constants, 9 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
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.
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.
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.
Clausius Parameter c - Clausius parameter c 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 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: 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
Reduced Molar Volume for Real Gas: 8.96 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Clausius Parameter c: 0.0002 --> No Conversion Required
Clausius Parameter b for Real Gas: 0.00243 --> No Conversion Required
Reduced Temperature: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T'c = (((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R]))/Tr --> (((0.8*4600000)+(0.1/((((8.96*11.5)+0.0002)^2))))*(((8.96*11.5)-0.00243)/[R]))/10
Evaluating ... ...
T'c = 4560466.20226662
STEP 3: Convert Result to Output's Unit
4560466.20226662 Kelvin --> No Conversion Required
FINAL ANSWER
4560466.20226662 ≈ 4.6E+6 Kelvin <-- Critical Temperature For Clausius Model
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Clausius Model of Real Gas » Critical Temperature » Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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10+ Critical Temperature Calculators

Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters
Go Critical Temperature For Clausius Model = (((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/((((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2))))*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature
Critical Temperature of Real Gas using Clausius Equation given Actual and Critical Parameters
Go Critical Temperature For Clausius Model = ((Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R]))/Temperature of Real Gas
Critical Temperature of Real Gas using Clausius Equation given Reduced and Actual Parameters
Go Critical Temperature For Clausius Model = ((Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature
Critical Temperature given Clausius Parameter b, Reduced and Actual Parameters
Go Critical Temperature For Clausius Model = ((Volume of Real Gas/Reduced Volume)-Clausius Parameter b for Real Gas)*((4*(Pressure/Reduced Pressure))/[R])
Critical Temperature given Clausius Parameter c, Reduced and Actual Parameters
Go Critical temperature given RP = ((Clausius Parameter c+(Volume of Real Gas/Reduced Volume))*8*(Pressure/Reduced Pressure))/(3*[R])
Critical Temperature of Real Gas given Clausius Parameter b
Go Critical Temperature For Clausius Model = (Critical Volume-Clausius Parameter b for Real Gas)*((4*Critical Pressure of Real Gas)/[R])
Critical Temperature of Real Gas given Clausius Parameter c
Go Critical Temperature For Clausius Model = ((Clausius Parameter c+Critical Volume)*8*Critical Pressure of Real Gas)/(3*[R])
Critical Temperature given Clausius Parameter a, Reduced and Actual Parameters
Go Critical Temperature For Clausius Model = ((Clausius Parameter a*64*(Pressure/Reduced Pressure))/(27*([R]^2)))^(1/3)
Critical Temperature of Real Gas given Clausius Parameter a
Go Critical Temperature For Clausius Model = ((Clausius Parameter a*64*Critical Pressure of Real Gas)/(27*([R]^2)))^(1/3)
Critical Temperature of Real Gas using Actual and Reduced Temperature
Go Critical Temperature For Clausius Model = Temperature of Real Gas/Reduced Temperature

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

Critical Temperature For Clausius Model = (((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/((((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2))))*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature
T'c = (((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R]))/Tr

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

Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters calculator uses Critical Temperature For Clausius Model = (((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/((((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2))))*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature to calculate the Critical Temperature For Clausius Model, The Critical Temperature of real gas using Clausius equation given reduced and critical parameters formula is defined as the highest temperature at which the substance can exist as a liquid. Critical Temperature For Clausius Model is denoted by T'c symbol.

How to calculate Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters, enter Reduced Pressure (Pr), Critical Pressure of Real Gas (P'c), Clausius Parameter a (a), Reduced Molar Volume for Real Gas (V'm,r), Critical Molar Volume (Vm,c), Clausius Parameter c (c), Clausius Parameter b for Real Gas (b') & Reduced Temperature (Tr) and hit the calculate button. Here is how the Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 5.7E+6 = (((0.8*4600000)+(0.1/((((8.96*11.5)+0.0002)^2))))*(((8.96*11.5)-0.00243)/[R]))/10.

FAQ

What is Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters?
The Critical Temperature of real gas using Clausius 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 = (((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R]))/Tr or Critical Temperature For Clausius Model = (((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/((((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2))))*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature. 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, 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, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole, Clausius parameter c 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 Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
How to calculate Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters?
The Critical Temperature of real gas using Clausius 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 For Clausius Model = (((Reduced Pressure*Critical Pressure of Real Gas)+(Clausius Parameter a/((((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2))))*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature. To calculate Critical Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters, you need Reduced Pressure (Pr), Critical Pressure of Real Gas (P'c), Clausius Parameter a (a), Reduced Molar Volume for Real Gas (V'm,r), Critical Molar Volume (Vm,c), Clausius Parameter c (c), Clausius Parameter b for Real Gas (b') & Reduced Temperature (Tr). With our tool, you need to enter the respective value for Reduced Pressure, Critical Pressure of Real Gas, Clausius Parameter a, Reduced Molar Volume for Real Gas, Critical Molar Volume, Clausius Parameter c, Clausius Parameter b for Real Gas & 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 For Clausius Model?
In this formula, Critical Temperature For Clausius Model uses Reduced Pressure, Critical Pressure of Real Gas, Clausius Parameter a, Reduced Molar Volume for Real Gas, Critical Molar Volume, Clausius Parameter c, Clausius Parameter b for Real Gas & Reduced Temperature. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Critical Temperature For Clausius Model = ((Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R]))/Temperature of Real Gas
  • Critical Temperature For Clausius Model = ((Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R]))/Reduced Temperature
  • Critical Temperature For Clausius Model = ((Clausius Parameter a*64*Critical Pressure of Real Gas)/(27*([R]^2)))^(1/3)
  • Critical Temperature For Clausius Model = (Critical Volume-Clausius Parameter b for Real Gas)*((4*Critical Pressure of Real Gas)/[R])
  • Critical Temperature For Clausius Model = ((Clausius Parameter c+Critical Volume)*8*Critical Pressure of Real Gas)/(3*[R])
  • Critical Temperature For Clausius Model = ((Clausius Parameter a*64*(Pressure/Reduced Pressure))/(27*([R]^2)))^(1/3)
  • Critical Temperature For Clausius Model = ((Volume of Real Gas/Reduced Volume)-Clausius Parameter b for Real Gas)*((4*(Pressure/Reduced Pressure))/[R])
  • Critical Temperature For Clausius Model = Temperature of Real Gas/Reduced Temperature
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