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Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Formula

GoDetermination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles Formula

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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. Check FAQs

A = - R \cdot T \cdot (\ln (\frac{[BoltZ] \cdot T}{p} \cdot {(\frac{2 \cdot π \cdot m \cdot [BoltZ] \cdot T}{{[hP]}^{2}})}^{\frac{3}{2}}) + 1)

A - Helmholtz Free Energy?R - Universal Gas Constant?T - Temperature?p - Pressure?m - Mass?[BoltZ] - Boltzmann constant?[BoltZ] - Boltzmann constant?[hP] - Planck constant?π - Archimedes' constant?

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Example

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Here is how the Determination of Helmholtz Free Energy using Sackur-Tetrode Equation equation looks like with Values.

Here is how the Determination of Helmholtz Free Energy using Sackur-Tetrode Equation equation looks like with Units.

Here is how the Determination of Helmholtz Free Energy using Sackur-Tetrode Equation equation looks like.

-39.0833 = - 8.314 \cdot 300 \cdot (\ln (\frac{1.4E-23 \cdot 300}{1.123} \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23 \cdot 300}{{6.6E-34}^{2}})}^{\frac{3}{2}}) + 1)

-39.0833KJ = - 8.314 \cdot 300K \cdot (\ln (\frac{1.4E-23J/K \cdot 300K}{1.123at} \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K \cdot 300K}{{6.6E-34}^{2}})}^{\frac{3}{2}}) + 1)

-39.0833 = - 8.314 \cdot 300 \cdot (\ln (\frac{1.4E-23 \cdot 300}{1.123} \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23 \cdot 300}{{6.6E-34}^{2}})}^{\frac{3}{2}}) + 1)

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Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Solution

Follow our step by step solution on how to calculate Determination of Helmholtz Free Energy using Sackur-Tetrode Equation?

FIRST Step Consider the formula

A = - R \cdot T \cdot (\ln (\frac{[BoltZ] \cdot T}{p} \cdot {(\frac{2 \cdot π \cdot m \cdot [BoltZ] \cdot T}{{[hP]}^{2}})}^{\frac{3}{2}}) + 1)

Next Step Substitute values of Variables

∴

A = - 8.314 \cdot 300K \cdot (\ln (\frac{[BoltZ] \cdot 300K}{1.123at} \cdot {(\frac{2 \cdot π \cdot 2.7E-26kg \cdot [BoltZ] \cdot 300K}{{[hP]}^{2}})}^{\frac{3}{2}}) + 1)

Next Step Substitute values of Constants

∴

A = - 8.314 \cdot 300K \cdot (\ln (\frac{1.4E-23J/K \cdot 300K}{1.123at} \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K \cdot 300K}{{6.6E-34}^{2}})}^{\frac{3}{2}}) + 1)

Next Step Convert Units

∴

A = - 8.314 \cdot 300K \cdot (\ln (\frac{1.4E-23J/K \cdot 300K}{110128.6795Pa} \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K \cdot 300K}{{6.6E-34}^{2}})}^{\frac{3}{2}}) + 1)

Next Step Prepare to Evaluate

∴

A = - 8.314 \cdot 300 \cdot (\ln (\frac{1.4E-23 \cdot 300}{110128.6795} \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23 \cdot 300}{{6.6E-34}^{2}})}^{\frac{3}{2}}) + 1)

Next Step Evaluate

∴

A = -39083.2773818438J

Next Step Convert to Output's Unit

∴

A = -39.0832773818438KJ

LAST Step Rounding Answer

∴

A = -39.0833KJ

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Formula Elements

Variables

Constants

Functions

Helmholtz Free Energy

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.

Symbol: A

Measurement: EnergyUnit: KJ

Note: Value can be positive or negative.

Formulas to find Helmholtz Free Energy

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.

Symbol: R

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Universal Gas Constant

Temperature

Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Pressure

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

Symbol: p

Measurement: PressureUnit: at

Note: Value can be positive or negative.

Formulas to find Pressure

Mass

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.

Symbol: m

Measurement: WeightUnit: kg

Note: Value can be positive or negative.

Formulas to find Mass

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Helmholtz Free Energy

Go Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles

A = - N A \cdot [BoltZ] \cdot T \cdot \ln (q)

Other formulas in Distinguishable Particles category

Go Total Number of Microstates in All Distributions

W tot = \frac{(N' + E - 1)!}{(N' - 1)! \cdot (E!)}

Go Translational Partition Function

q trans = V \cdot {(\frac{2 \cdot π \cdot m \cdot [BoltZ] \cdot T}{{[hP]}^{2}})}^{\frac{3}{2}}

Go Translational Partition Function using Thermal de Broglie Wavelength

q trans = \frac{V}{{(Λ)}^{3}}

Go Determination of Entropy using Sackur-Tetrode Equation

S° m = R \cdot (- 1.154 + (\frac{3}{2}) \cdot \ln (A r) + (\frac{5}{2}) \cdot \ln (T) - \ln (\frac{p}{p°}))

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

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation evaluator uses Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1) to evaluate 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 evaluate Determination of Helmholtz Free Energy using Sackur-Tetrode Equation using this online evaluator? To use this online evaluator 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.

FAQs on Determination of Helmholtz Free Energy using Sackur-Tetrode Equation

What is the formula to find Determination of Helmholtz Free Energy using Sackur-Tetrode Equation?

The formula of Determination of Helmholtz Free Energy using Sackur-Tetrode Equation is expressed as Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1). Here is an example- -0.155302 = -8.314*300*(ln(([BoltZ]*300)/110128.6795*((2*pi*2.656E-26*[BoltZ]*300)/[hP]^2)^(3/2))+1).

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

With Universal Gas Constant (R), Temperature (T), Pressure (p) & Mass (m) we can find Determination of Helmholtz Free Energy using Sackur-Tetrode Equation using the formula - Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1). This formula also uses Boltzmann constant, Boltzmann constant, Planck constant, Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Helmholtz Free Energy?

Here are the different ways to Calculate Helmholtz Free Energy-

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

Can the Determination of Helmholtz Free Energy using Sackur-Tetrode Equation be negative?

Yes, the Determination of Helmholtz Free Energy using Sackur-Tetrode Equation, measured in Energy can be negative.

Which unit is used to measure Determination of Helmholtz Free Energy using Sackur-Tetrode Equation?

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Determination of Helmholtz Free Energy using Sackur-Tetrode Equation can be measured.

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Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Formula

​GoDetermination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles Formula

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Example

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Solution

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation Formula Elements

Other Formulas to find Helmholtz Free Energy

Other formulas in Distinguishable Particles category

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

FAQs on Determination of Helmholtz Free Energy using Sackur-Tetrode Equation

Variable Name

GoDetermination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles Formula