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Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters Calculator

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✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]
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-10%
✖Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.ⓘ Pressure [p]
+10%
-10%
✖Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure [Pc]
+10%
-10%
✖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.ⓘ Critical Temperature [Tc]
+10%
-10%
✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [Vm,c]
+10%
-10%
✖Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.ⓘ Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters [Vm,r]
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Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters

Formula
`"V"_{"m,r"} = (("[R]"*"T"/"p")*(1+(((9*"p"/"P"_{"c"})/(128*"T"/"T"_{"c"}))*(1-(6/(("T"^2)/("T"_{"c"}^2)))))))/"V"_{"m,c"}`

Example
`"-52.221478"=(("[R]"*"85K"/"800Pa")*(1+(((9*"800Pa"/"218Pa")/(128*"85K"/"647K"))*(1-(6/((("85K")^2)/(("647K")^2)))))))/"11.5m³/mol"`

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Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
Vm,r = (([R]*T/p)*(1+(((9*p/Pc)/(128*T/Tc))*(1-(6/((T^2)/(Tc^2)))))))/Vm,c
This formula uses 1 Constants, 6 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
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.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Pressure - (Measured in Pascal) - Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Critical Temperature - (Measured in Kelvin) - 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.
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
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Pressure: 800 Pascal --> 800 Pascal No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Critical Temperature: 647 Kelvin --> 647 Kelvin 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
Vm,r = (([R]*T/p)*(1+(((9*p/Pc)/(128*T/Tc))*(1-(6/((T^2)/(Tc^2)))))))/Vm,c --> (([R]*85/800)*(1+(((9*800/218)/(128*85/647))*(1-(6/((85^2)/(647^2)))))))/11.5
Evaluating ... ...
Vm,r = -52.221478246999
STEP 3: Convert Result to Output's Unit
-52.221478246999 --> No Conversion Required
FINAL ANSWER
-52.221478246999 ≈ -52.221478 <-- Reduced Molar Volume
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Berthelot and Modified Berthelot Model of Real Gas » Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters

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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))

Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters Formula

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
Vm,r = (([R]*T/p)*(1+(((9*p/Pc)/(128*T/Tc))*(1-(6/((T^2)/(Tc^2)))))))/Vm,c

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 using Modified Berthelot Equation given Critical and Actual Parameters?

Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters calculator uses 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 to calculate the Reduced Molar Volume, The Reduced Molar Volume using Modified Berthelot equation given critical and actual 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 is denoted by Vm,r symbol.

How to calculate Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters using this online calculator? To use this online calculator for Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters, enter Temperature (T), Pressure (p), Critical Pressure (Pc), Critical Temperature (Tc) & Critical Molar Volume (Vm,c) and hit the calculate button. Here is how the Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters calculation can be explained with given input values -> -52.221478 = (([R]*85/800)*(1+(((9*800/218)/(128*85/647))*(1-(6/((85^2)/(647^2)))))))/11.5.

FAQ

What is Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters?
The Reduced Molar Volume using Modified Berthelot equation given critical and actual 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 Vm,r = (([R]*T/p)*(1+(((9*p/Pc)/(128*T/Tc))*(1-(6/((T^2)/(Tc^2)))))))/Vm,c or 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 is the degree or intensity of heat present in a substance or object, Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed, Critical Pressure is the minimum pressure required to liquify a substance at the 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 & Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.
How to calculate Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters?
The Reduced Molar Volume using Modified Berthelot equation given critical and actual 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 = (([R]*Temperature/Pressure)*(1+(((9*Pressure/Critical Pressure)/(128*Temperature/Critical Temperature))*(1-(6/((Temperature^2)/(Critical Temperature^2)))))))/Critical Molar Volume. To calculate Reduced Molar Volume using Modified Berthelot Equation given Critical and Actual Parameters, you need Temperature (T), Pressure (p), Critical Pressure (Pc), Critical Temperature (Tc) & Critical Molar Volume (Vm,c). With our tool, you need to enter the respective value for Temperature, Pressure, Critical Pressure, Critical Temperature & Critical Molar Volume and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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