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

STEP 0: Pre-Calculation Summary
Formula Used
Temperature given CE = ((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])
TCE = ((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R])
This formula uses 1 Constants, 8 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Temperature given CE - (Measured in Kelvin) - Temperature given CE is the degree or intensity of heat present in a substance or object.
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.
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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TCE = ((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R]) --> ((0.8*4600000)+(0.1/((((8.96*11.5)+0.0002)^2))))*(((8.96*11.5)-0.00243)/[R])
Evaluating ... ...
TCE = 45604662.0226662
STEP 3: Convert Result to Output's Unit
45604662.0226662 Kelvin --> No Conversion Required
FINAL ANSWER
45604662.0226662 4.6E+7 Kelvin <-- Temperature given CE
(Calculation completed in 00.020 seconds)

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4 Pressure and Temperature of Real Gas Calculators

Pressure of Real Gas using Clausius Equation given Reduced and Critical Parameters
Go Pressure = (([R]*(Reduced Temperature*Critical Temperature For Clausius Model))/((Reduced Molar Volume for Real Gas*Critical Molar Volume)-Clausius Parameter b for Real Gas))-(Clausius Parameter a/((Reduced Temperature*Critical Temperature For Clausius Model)*(((Reduced Molar Volume for Real Gas*Critical Molar Volume)+Clausius Parameter c)^2)))
Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters
Go Temperature given CE = ((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])
Pressure of Real Gas using Clausius Equation
Go Pressure = (([R]*Temperature of Real Gas)/(Molar Volume-Clausius Parameter b for Real Gas))-(Clausius Parameter a/(Temperature of Real Gas*((Molar Volume+Clausius Parameter c)^2)))
Temperature of Real Gas using Clausius Equation
Go Temperature given CE = (Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R])

19 Important Formulae on Clausius Model of Real Gas Calculators

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

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

Temperature given CE = ((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])
TCE = ((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[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 Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters?

Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters calculator uses Temperature given CE = ((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]) to calculate the Temperature given CE, The Temperature of real gas using Clausius equation given reduced and critical parameters formula is defined as the degree or intensity of heat present in a substance or object. Temperature given CE is denoted by TCE symbol.

How to calculate Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for 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') and hit the calculate button. Here is how the Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 5.7E+7 = ((0.8*4600000)+(0.1/((((8.96*11.5)+0.0002)^2))))*(((8.96*11.5)-0.00243)/[R]) .

FAQ

What is Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters?
The Temperature of real gas using Clausius equation given reduced and critical parameters formula is defined as the degree or intensity of heat present in a substance or object and is represented as TCE = ((Pr*P'c)+(a/((((V'm,r*Vm,c)+c)^2))))*(((V'm,r*Vm,c)-b')/[R]) or Temperature given CE = ((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 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.
How to calculate Temperature of Real Gas using Clausius Equation given Reduced and Critical Parameters?
The Temperature of real gas using Clausius equation given reduced and critical parameters formula is defined as the degree or intensity of heat present in a substance or object is calculated using Temperature given CE = ((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]). To calculate 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'). 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 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 Temperature given CE?
In this formula, Temperature given CE 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. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Temperature given CE = (Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R])
  • Temperature given CE = (Pressure+(Clausius Parameter a/(((Molar Volume+Clausius Parameter c)^2))))*((Molar Volume-Clausius Parameter b for Real Gas)/[R])
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