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Translational Partition Function Formula

GoTranslational Partition Function using Thermal de Broglie Wavelength Formula

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Translational Partition Function is the contribution to the total partition function due to translational motion. Check FAQs

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

q_trans - Translational Partition Function?V - Volume?m - Mass?T - Temperature?[BoltZ] - Boltzmann constant?[hP] - Planck constant?π - Archimedes' constant?

Translational Partition Function Example

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Here is how the Translational Partition Function equation looks like with Values.

Here is how the Translational Partition Function equation looks like with Units.

Here is how the Translational Partition Function equation looks like.

1.4E+30 = 0.0221 \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23 \cdot 300}{{6.6E-34}^{2}})}^{\frac{3}{2}}

1.4E+30 = 0.0221m³ \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K \cdot 300K}{{6.6E-34}^{2}})}^{\frac{3}{2}}

1.4E+30 = 0.0221 \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23 \cdot 300}{{6.6E-34}^{2}})}^{\frac{3}{2}}

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Translational Partition Function Solution

Follow our step by step solution on how to calculate Translational Partition Function?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

q trans = 0.0221m³ \cdot {(\frac{2 \cdot π \cdot 2.7E-26kg \cdot [BoltZ] \cdot 300K}{{[hP]}^{2}})}^{\frac{3}{2}}

Next Step Substitute values of Constants

∴

q trans = 0.0221m³ \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K \cdot 300K}{{6.6E-34}^{2}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

q trans = 0.0221 \cdot {(\frac{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23 \cdot 300}{{6.6E-34}^{2}})}^{\frac{3}{2}}

Next Step Evaluate

∴

q trans = 1.3830186546575E+30

LAST Step Rounding Answer

∴

q trans = 1.4E+30

Translational Partition Function Formula Elements

Variables

Constants

Translational Partition Function

Translational Partition Function is the contribution to the total partition function due to translational motion.

Symbol: q_trans

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Translational Partition Function

Volume

Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Volume

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

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

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

Other Formulas to find Translational Partition Function

Go Translational Partition Function using Thermal de Broglie Wavelength

q trans = \frac{V}{{(Λ)}^{3}}

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 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°}))

Go Determination of Helmholtz Free Energy using Sackur-Tetrode Equation

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)

Go Determination of Gibbs Free Energy using Sackur-Tetrode Equation

G = - 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}})

How to Evaluate Translational Partition Function?

Translational Partition Function evaluator uses Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2) to evaluate the Translational Partition Function, The Translational Partition Function formula is defined as the contribution to the total partition function due to translational motion. Translational Partition Function is denoted by q_trans symbol.

How to evaluate Translational Partition Function using this online evaluator? To use this online evaluator for Translational Partition Function, enter Volume (V), Mass (m) & Temperature (T) and hit the calculate button.

FAQs on Translational Partition Function

What is the formula to find Translational Partition Function?

The formula of Translational Partition Function is expressed as Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2). Here is an example- 8.4E+30 = 0.02214*((2*pi*2.656E-26*[BoltZ]*300)/([hP]^2))^(3/2).

How to calculate Translational Partition Function?

With Volume (V), Mass (m) & Temperature (T) we can find Translational Partition Function using the formula - Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2). This formula also uses Boltzmann constant, Planck constant, Archimedes' constant .

What are the other ways to Calculate Translational Partition Function?

Here are the different ways to Calculate Translational Partition Function-

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

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Translational Partition Function Formula

​GoTranslational Partition Function using Thermal de Broglie Wavelength Formula

Translational Partition Function Example

Translational Partition Function Solution

Translational Partition Function Formula Elements

Other Formulas to find Translational Partition Function

Other formulas in Distinguishable Particles category

How to Evaluate Translational Partition Function?

FAQs on Translational Partition Function

Variable Name

GoTranslational Partition Function using Thermal de Broglie Wavelength Formula