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

STEP 0: Pre-Calculation Summary
Formula Used
Temperature = ((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/(Reduced Molar Volume*Critical Molar Volume)))/([R]/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b))
T = ((Pr*Pc)+(a/(Vm,r*Vm,c)))/([R]/((Vm,r*Vm,c)-b))
This formula uses 1 Constants, 7 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Temperature - (Measured in Kelvin) - Temperature 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 - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Berthelot Parameter a - Berthelot parameter a is an empirical parameter characteristic to equation obtained from Berthelot model of real gas.
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.
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.
Berthelot Parameter b - Berthelot parameter b is an empirical parameter characteristic to equation obtained from Berthelot model of real gas.
STEP 1: Convert Input(s) to Base Unit
Reduced Pressure: 3.675E-05 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Berthelot Parameter a: 0.1 --> No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Berthelot Parameter b: 0.2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = ((Pr*Pc)+(a/(Vm,r*Vm,c)))/([R]/((Vm,r*Vm,c)-b)) --> ((3.675E-05*218)+(0.1/(11.2*11.5)))/([R]/((11.2*11.5)-0.2))
Evaluating ... ...
T = 0.135922629326573
STEP 3: Convert Result to Output's Unit
0.135922629326573 Kelvin --> No Conversion Required
FINAL ANSWER
0.135922629326573 0.135923 Kelvin <-- Temperature
(Calculation completed in 00.019 seconds)

Credits

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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21 Berthelot and Modified Berthelot Model of Real Gas Calculators

Molar Volume using Modified Berthelot Equation given Critical and Reduced Parameters
Go Molar Volume = ([R]*(Reduced Temperature*Critical Temperature)/(Reduced Pressure*Critical Pressure))*(1+(((9*(Reduced Pressure*Critical Pressure)/Critical Pressure)/(128*(Reduced Temperature*Critical Temperature)/Critical Temperature))*(1-(6/(((Reduced Temperature*Critical Temperature)^2)/(Critical Temperature^2))))))
Berthelot Parameter b of Real Gas given Critical and Reduced Parameters
Go Berthelot Parameter b = (Reduced Molar Volume*Critical Molar Volume)-(([R]*(Reduced Temperature*Critical Temperature))/((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/((Reduced Temperature*Critical Temperature)*((Reduced Molar Volume*Critical Molar Volume)^2)))))
Berthelot Parameter of Real Gas given Critical and Reduced Parameters
Go Berthelot Parameter a = ((([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b))-(Reduced Pressure*Critical Pressure))*((Reduced Temperature*Critical Temperature)*((Reduced Molar Volume*Critical Molar Volume)^2))
Molar Volume of Real Gas using Berthelot Equation given Critical and Reduced Parameters
Go Molar Volume = ((1/(Reduced Pressure*Critical Pressure))+(Berthelot Parameter b/([R]*(Reduced Temperature*Critical Temperature))))/((1/([R]*(Reduced Temperature*Critical Temperature)))-((Reduced Temperature*Critical Temperature)/Berthelot Parameter a))
Pressure of Real Gas using Berthelot Equation given Critical and Reduced Parameters
Go Pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b))-(Berthelot Parameter a/((Reduced Temperature*Critical Temperature)*((Reduced Molar Volume*Critical Molar Volume)^2)))
Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters
Go Reduced Molar Volume = (([R]*Temperature/Pressure)*(1+(((9*Pressure/Critical Pressure)/(128*Temperature/Critical Temperature))*(1-(6/((Temperature^2)/(Critical Temperature^2)))))))/Critical Molar Volume
Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters
Go Temperature = ((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/(Reduced Molar Volume*Critical Molar Volume)))/([R]/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b))
Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters
Go Molar Volume = ([R]*Temperature/Pressure)*(1+(((9*Pressure/Critical Pressure)/(128*Temperature/Critical Temperature))*(1-(6/((Temperature^2)/(Critical Temperature^2))))))
Critical Pressure using Modified Berthelot Equation given Reduced and Actual Parameters
Go Critical Pressure = 9/128*(Pressure of Gas/Reduced Temperature)*((1-(6/(Reduced Temperature^2)))/(((Pressure of Gas*Molar Volume of Real Gas)/([R]*Temperature of Real Gas))-1))
Molar Volume of Real Gas using Berthelot Equation
Go Molar Volume = ((1/Pressure)+(Berthelot Parameter b/([R]*Temperature)))/((1/([R]*Temperature))-(Temperature/Berthelot Parameter a))
Critical Molar Volume using Modified Berthelot Equation given Reduced and Actual Parameters
Go Critical Molar Volume = (([R]*Temperature/Pressure)*(1+(((9*Reduced Pressure)/(128*Reduced Temperature))*(1-(6/((Reduced Temperature^2)))))))/Reduced Molar Volume
Reduced Pressure using Modified Berthelot Equation given Actual Parameters
Go Reduced Pressure = 128/9*Reduced Temperature*((((Pressure of Gas*Molar Volume of Real Gas)/([R]*Temperature of Real Gas))-1)/(1-(6/(Reduced Temperature^2))))
Pressure of Real Gas using Berthelot Equation
Go Pressure = (([R]*Temperature)/(Molar Volume-Berthelot Parameter b))-(Berthelot Parameter a/(Temperature*(Molar Volume^2)))
Berthelot parameter b of Real Gas
Go Berthelot Parameter b = Molar Volume-(([R]*Temperature)/(Pressure+(Berthelot Parameter a/(Temperature*(Molar Volume^2)))))
Berthelot Parameter of Real Gas
Go Berthelot Parameter a = ((([R]*Temperature)/(Molar Volume-Berthelot Parameter b))-Pressure)*(Temperature*(Molar Volume^2))
Molar Volume using Modified Berthelot Equation given Reduced and Actual Parameters
Go Molar Volume = ([R]*Temperature/Pressure)*(1+(((9* Reduced Pressure)/(128*Reduced Temperature))*(1-(6/((Reduced Temperature^2))))))
Temperature using Modified Berthelot Equation given Reduced and Actual Parameters
Go Temperature = (Pressure*Molar Volume/[R])/(1+(((9* Reduced Pressure)/(128*Reduced Temperature))*(1-(6/((Reduced Temperature^2))))))
Pressure using Modified Berthelot Equation given Reduced and Actual Parameters
Go Pressure = ([R]*Temperature/Molar Volume)*(1+(((9* Reduced Pressure)/(128*Reduced Temperature))*(1-(6/((Reduced Temperature^2))))))
Critical Temperature using Modified Berthelot Equation given Reduced and Actual Parameters
Go Critical Temperature of Real Gases = Temperature/(((9*Reduced Pressure)/128)/(((Pressure*Volume)/([R]*Temperature))-1))
Reduced Temperature using Modified Berthelot Equation given Actual Parameters
Go Reduced Temperature in Real Gases = ((9*Reduced Pressure)/128)/(((Pressure of Gas*Molar Volume of Real Gas)/([R]*Temperature of Real Gas))-1)
Temperature of Real Gas using Berthelot Equation
Go Temperature = (Pressure+(Berthelot Parameter a/Molar Volume))/([R]/(Molar Volume-Berthelot Parameter b))

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

Temperature = ((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/(Reduced Molar Volume*Critical Molar Volume)))/([R]/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b))
T = ((Pr*Pc)+(a/(Vm,r*Vm,c)))/([R]/((Vm,r*Vm,c)-b))

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 Berthelot Equation given Critical and Reduced Parameters?

Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters calculator uses Temperature = ((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/(Reduced Molar Volume*Critical Molar Volume)))/([R]/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b)) to calculate the Temperature, The Temperature of Real Gas using Berthelot equation given critical and reduced parameters is the degree or intensity of heat present in the volume of real gas. Temperature is denoted by T symbol.

How to calculate Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters using this online calculator? To use this online calculator for Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters, enter Reduced Pressure (Pr), Critical Pressure (Pc), Berthelot Parameter a (a), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c) & Berthelot Parameter b (b) and hit the calculate button. Here is how the Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters calculation can be explained with given input values -> 0.135923 = ((3.675E-05*218)+(0.1/(11.2*11.5)))/([R]/((11.2*11.5)-0.2)).

FAQ

What is Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters?
The Temperature of Real Gas using Berthelot equation given critical and reduced parameters is the degree or intensity of heat present in the volume of real gas and is represented as T = ((Pr*Pc)+(a/(Vm,r*Vm,c)))/([R]/((Vm,r*Vm,c)-b)) or Temperature = ((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/(Reduced Molar Volume*Critical Molar Volume)))/([R]/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b)). Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature, Berthelot parameter a is an empirical parameter characteristic to equation obtained from Berthelot model of real gas, Reduced Molar Volume 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 & Berthelot parameter b is an empirical parameter characteristic to equation obtained from Berthelot model of real gas.
How to calculate Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters?
The Temperature of Real Gas using Berthelot equation given critical and reduced parameters is the degree or intensity of heat present in the volume of real gas is calculated using Temperature = ((Reduced Pressure*Critical Pressure)+(Berthelot Parameter a/(Reduced Molar Volume*Critical Molar Volume)))/([R]/((Reduced Molar Volume*Critical Molar Volume)-Berthelot Parameter b)). To calculate Temperature of Real Gas using Berthelot Equation given Critical and Reduced Parameters, you need Reduced Pressure (Pr), Critical Pressure (Pc), Berthelot Parameter a (a), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c) & Berthelot Parameter b (b). With our tool, you need to enter the respective value for Reduced Pressure, Critical Pressure, Berthelot Parameter a, Reduced Molar Volume, Critical Molar Volume & Berthelot Parameter b 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?
In this formula, Temperature uses Reduced Pressure, Critical Pressure, Berthelot Parameter a, Reduced Molar Volume, Critical Molar Volume & Berthelot Parameter b. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Temperature = (Pressure+(Berthelot Parameter a/Molar Volume))/([R]/(Molar Volume-Berthelot Parameter b))
  • Temperature = (Pressure*Molar Volume/[R])/(1+(((9* Reduced Pressure)/(128*Reduced Temperature))*(1-(6/((Reduced Temperature^2))))))
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