HCF of three numbers

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Calculator

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✖Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joulekelvin−1mole−1.ⓘ Universal Gas Constant [R]			+10% -10%
✖Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.ⓘ Temperature [T]			+10% -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%
✖Mass is the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field.ⓘ Mass [m]			+10% -10%

✖Helmholtz Free Energy is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential.ⓘ Determination of Helmholtz Free Energy using Sackur-Tetrode Equation [A]

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Determination of Helmholtz Free Energy using Sackur-Tetrode Equation

Formula

`"A" = -"R"*"T"*(ln(("[BoltZ]"*"T")/"p"*((2*pi*"m"*"[BoltZ]"*"T")/"[hP]"^2)^(3/2))+1)`

Example

`"-39.083277KJ"=-"8.314"*"300K"*(ln(("[BoltZ]"*"300K")/"1.123at"*((2*pi*"26.56E^-27kg"*"[BoltZ]"*"300K")/"[hP]"^2)^(3/2))+1)`

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Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1)
A = -R*T*(ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2))+1)
This formula uses 3 Constants, 1 Functions, 5 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Helmholtz Free Energy - (Measured in Joule) - Helmholtz Free Energy is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential.
Universal Gas Constant - Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1.
Temperature - (Measured in Kelvin) - Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.
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.
Mass - (Measured in Kilogram) - Mass is the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field.

STEP 1: Convert Input(s) to Base Unit

Universal Gas Constant: 8.314 --> No Conversion Required
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Pressure: 1.123 Atmosphere Technical --> 110128.6795 Pascal (Check conversion here)
Mass: 2.656E-26 Kilogram --> 2.656E-26 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = -R*T*(ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2))+1) --> -8.314*300*(ln(([BoltZ]*300)/110128.6795*((2*pi*2.656E-26*[BoltZ]*300)/[hP]^2)^(3/2))+1)

Evaluating ... ...

A = -39083.2773818438

STEP 3: Convert Result to Output's Unit

-39083.2773818438 Joule -->-39.0832773818438 Kilojoule (Check conversion here)

FINAL ANSWER

-39.0832773818438 ≈ -39.083277 Kilojoule <-- Helmholtz Free Energy

(Calculation completed in 00.004 seconds)

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Determination of Helmholtz Free Energy using Sackur-Tetrode Equation

Go Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1)

Determination of Gibbs Free Energy using Sackur-Tetrode Equation

Go Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))

Determination of Entropy using Sackur-Tetrode Equation

Go Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure))

Determination of Gibbs Free energy using Molecular PF for Distinguishable Particles

Go Gibbs Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)+Pressure*Volume

Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles

Go Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1)

Determination of Gibbs Free energy using Molecular PF for Indistinguishable Particles

Go Gibbs Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function/Number of Atoms or Molecules)

Total Number of Microstates in All Distributions

Go Total Number of Microstates = ((Total Number of Particles+Number of Quanta of Energy-1)!)/((Total Number of Particles-1)!*(Number of Quanta of Energy!))

Vibrational Partition Function for Diatomic Ideal Gas

Go Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature)))

Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles

Go Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)

Translational Partition Function

Go Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2)

Rotational Partition Function for Homonuclear Diatomic Molecules

Go Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)

Rotational Partition Function for Heteronuclear Diatomic Molecule

Go Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)

Mathematical Probability of Occurrence of Distribution

Go Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates

Boltzmann-Planck Equation

Go Entropy = [BoltZ]*ln(Number of Microstates in a Distribution)

Translational Partition Function using Thermal de Broglie Wavelength

Go Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Formula

What is Statistical Thermodynamics?

Statistical thermodynamics is a theory that uses molecular properties to predict the behavior of macroscopic quantities of compounds. While the origins of statistical thermodynamics predate the development of quantum mechanics, the modern development of statistical thermodynamics assumes that the quantized energy levels associated with a particular system are known. From these energy-level data, a temperature-dependent quantity called the partition function can be calculated. From the partition function, all of the thermodynamic properties of the system can be calculated. Statistical thermodynamics has also been applied to the general problem of predicting reaction rates. This application is called transition state theory or the theory of absolute reaction rates.

How to Calculate Determination of Helmholtz Free Energy using Sackur-Tetrode Equation?

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation calculator uses Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1) to calculate the Helmholtz Free Energy, The Determination of Helmholtz Free Energy using Sackur-Tetrode Equation formula is defined as is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential. Helmholtz Free Energy is denoted by A symbol.

How to calculate Determination of Helmholtz Free Energy using Sackur-Tetrode Equation using this online calculator? To use this online calculator for Determination of Helmholtz Free Energy using Sackur-Tetrode Equation, enter Universal Gas Constant (R), Temperature (T), Pressure (p) & Mass (m) and hit the calculate button. Here is how the Determination of Helmholtz Free Energy using Sackur-Tetrode Equation calculation can be explained with given input values -> -0.039083 = -8.314*300*(ln(([BoltZ]*300)/110128.6795*((2*pi*2.656E-26*[BoltZ]*300)/[hP]^2)^(3/2))+1).

FAQ

What is Determination of Helmholtz Free Energy using Sackur-Tetrode Equation?

The Determination of Helmholtz Free Energy using Sackur-Tetrode Equation formula is defined as is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential and is represented as A = -R*T*(ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2))+1) or Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1). Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1, Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin, Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed & Mass is the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field.

How to calculate Determination of Helmholtz Free Energy using Sackur-Tetrode Equation?

The Determination of Helmholtz Free Energy using Sackur-Tetrode Equation formula is defined as is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential is calculated using Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1). To calculate Determination of Helmholtz Free Energy using Sackur-Tetrode Equation, you need Universal Gas Constant (R), Temperature (T), Pressure (p) & Mass (m). With our tool, you need to enter the respective value for Universal Gas Constant, Temperature, Pressure & Mass 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 Helmholtz Free Energy?

In this formula, Helmholtz Free Energy uses Universal Gas Constant, Temperature, Pressure & Mass. We can use 2 other way(s) to calculate the same, which is/are as follows -

Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)
Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1)

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