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Translational Partition Function using Thermal de Broglie Wavelength Calculator

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✖Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.ⓘ Volume [V]			+10% -10%
✖Thermal de Broglie Wavelength is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature.ⓘ Thermal de Broglie Wavelength [Λ]			+10% -10%

✖Translational Partition Function is the contribution to the total partition function due to translational motion.ⓘ Translational Partition Function using Thermal de Broglie Wavelength [q_trans]

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Formula

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Translational Partition Function using Thermal de Broglie Wavelength

Formula

`"q"_{"trans"} = "V"/("Λ")^3`

Example

`"1.4E^30"="0.02214m³"/("2.52E^-11m")^3`

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Translational Partition Function using Thermal de Broglie Wavelength Solution

STEP 0: Pre-Calculation Summary

Formula Used

Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3
q_trans = V/(Λ)^3
This formula uses 3 Variables

Variables Used

Translational Partition Function - Translational Partition Function is the contribution to the total partition function due to translational motion.
Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.
Thermal de Broglie Wavelength - (Measured in Meter) - Thermal de Broglie Wavelength is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature.

STEP 1: Convert Input(s) to Base Unit

Volume: 0.02214 Cubic Meter --> 0.02214 Cubic Meter No Conversion Required
Thermal de Broglie Wavelength: 2.52E-11 Meter --> 2.52E-11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_trans = V/(Λ)^3 --> 0.02214/(2.52E-11)^3

Evaluating ... ...

q_trans = 1.38348990389807E+30

STEP 3: Convert Result to Output's Unit

1.38348990389807E+30 --> No Conversion Required

FINAL ANSWER

1.38348990389807E+30 ≈ 1.4E+30 <-- Translational Partition Function

(Calculation completed in 00.004 seconds)

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< 15 Statistical Thermodynamics Calculators

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

Translational Partition Function using Thermal de Broglie Wavelength Formula

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

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 Translational Partition Function using Thermal de Broglie Wavelength?

Translational Partition Function using Thermal de Broglie Wavelength calculator uses Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3 to calculate the Translational Partition Function, The Translational Partition Function using Thermal de Broglie Wavelength formula is defined as contribution to the total partition function due to translational motion where de broglie wavelength is involved. Translational Partition Function is denoted by q_trans symbol.

How to calculate Translational Partition Function using Thermal de Broglie Wavelength using this online calculator? To use this online calculator for Translational Partition Function using Thermal de Broglie Wavelength, enter Volume (V) & Thermal de Broglie Wavelength (Λ) and hit the calculate button. Here is how the Translational Partition Function using Thermal de Broglie Wavelength calculation can be explained with given input values -> 1.4E+30 = 0.02214/(2.52E-11)^3.

FAQ

What is Translational Partition Function using Thermal de Broglie Wavelength?

The Translational Partition Function using Thermal de Broglie Wavelength formula is defined as contribution to the total partition function due to translational motion where de broglie wavelength is involved and is represented as q_trans = V/(Λ)^3 or Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3. Volume is the amount of space that a substance or object occupies, or that is enclosed within a container & Thermal de Broglie Wavelength is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature.

How to calculate Translational Partition Function using Thermal de Broglie Wavelength?

The Translational Partition Function using Thermal de Broglie Wavelength formula is defined as contribution to the total partition function due to translational motion where de broglie wavelength is involved is calculated using Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3. To calculate Translational Partition Function using Thermal de Broglie Wavelength, you need Volume (V) & Thermal de Broglie Wavelength (Λ). With our tool, you need to enter the respective value for Volume & Thermal de Broglie Wavelength 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 Translational Partition Function?

In this formula, Translational Partition Function uses Volume & Thermal de Broglie Wavelength. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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