HCF of two numbers

Boltzmann-Planck Equation Calculator

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✖Number of Microstates in a Distribution describes the precise positions and momenta of all the individual particles or components that make up the distribution.ⓘ Number of Microstates in a Distribution [W]

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✖Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty.ⓘ Boltzmann-Planck Equation [S]

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Formula

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Boltzmann-Planck Equation

Formula

`"S" = "[BoltZ]"*ln("W")`

Example

`"4.7E^-23J/K"="[BoltZ]"*ln("30")`

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Boltzmann-Planck Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Entropy = [BoltZ]*ln(Number of Microstates in a Distribution)
S = [BoltZ]*ln(W)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

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

Entropy - (Measured in Joule per Kelvin) - Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty.
Number of Microstates in a Distribution - Number of Microstates in a Distribution describes the precise positions and momenta of all the individual particles or components that make up the distribution.

STEP 1: Convert Input(s) to Base Unit

Number of Microstates in a Distribution: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = [BoltZ]*ln(W) --> [BoltZ]*ln(30)

Evaluating ... ...

S = 4.69585813121973E-23

STEP 3: Convert Result to Output's Unit

4.69585813121973E-23 Joule per Kelvin --> No Conversion Required

FINAL ANSWER

4.69585813121973E-23 ≈ 4.7E-23 Joule per Kelvin <-- Entropy

(Calculation completed in 00.005 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

Boltzmann-Planck Equation Formula

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

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 Boltzmann-Planck Equation?

Boltzmann-Planck Equation calculator uses Entropy = [BoltZ]*ln(Number of Microstates in a Distribution) to calculate the Entropy, The Boltzmann-Planck Equation formula is defined as a probability equation relating the entropy a probability equation relating the entropy , also written as , of an ideal gas to the multiplicity(W), the number of real microstates corresponding to a gas's macrostate. Entropy is denoted by S symbol.

How to calculate Boltzmann-Planck Equation using this online calculator? To use this online calculator for Boltzmann-Planck Equation, enter Number of Microstates in a Distribution (W) and hit the calculate button. Here is how the Boltzmann-Planck Equation calculation can be explained with given input values -> 4.7E-23 = [BoltZ]*ln(30).

FAQ

What is Boltzmann-Planck Equation?

The Boltzmann-Planck Equation formula is defined as a probability equation relating the entropy a probability equation relating the entropy , also written as , of an ideal gas to the multiplicity(W), the number of real microstates corresponding to a gas's macrostate and is represented as S = [BoltZ]*ln(W) or Entropy = [BoltZ]*ln(Number of Microstates in a Distribution). Number of Microstates in a Distribution describes the precise positions and momenta of all the individual particles or components that make up the distribution.

How to calculate Boltzmann-Planck Equation?

The Boltzmann-Planck Equation formula is defined as a probability equation relating the entropy a probability equation relating the entropy , also written as , of an ideal gas to the multiplicity(W), the number of real microstates corresponding to a gas's macrostate is calculated using Entropy = [BoltZ]*ln(Number of Microstates in a Distribution). To calculate Boltzmann-Planck Equation, you need Number of Microstates in a Distribution (W). With our tool, you need to enter the respective value for Number of Microstates in a Distribution 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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