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Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Formula

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Energy of i-th State is defined as the total quantity of energy present in a particular energy state. Check FAQs

ε i = \frac{1}{β} \cdot (\ln (\frac{g}{n i}) - α)

ε_i - Energy of i-th State?β - Lagrange's Undetermined Multiplier 'β'?g - Number of Degenerate States?n_i - Number of particles in i-th State?α - Lagrange's Undetermined Multiplier 'α'?

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Example

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Here is how the Determination of Energy of I-th State for Maxwell-Boltzmann Statistics equation looks like with Values.

Here is how the Determination of Energy of I-th State for Maxwell-Boltzmann Statistics equation looks like with Units.

Here is how the Determination of Energy of I-th State for Maxwell-Boltzmann Statistics equation looks like.

40054.5753 = \frac{1}{0.0001} \cdot (\ln (\frac{3}{0.0002}) - 5.0324)

40054.5753J = \frac{1}{0.0001J} \cdot (\ln (\frac{3}{0.0002}) - 5.0324)

40054.5753 = \frac{1}{0.0001} \cdot (\ln (\frac{3}{0.0002}) - 5.0324)

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Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Solution

Follow our step by step solution on how to calculate Determination of Energy of I-th State for Maxwell-Boltzmann Statistics?

FIRST Step Consider the formula

ε i = \frac{1}{β} \cdot (\ln (\frac{g}{n i}) - α)

Next Step Substitute values of Variables

∴

ε i = \frac{1}{0.0001J} \cdot (\ln (\frac{3}{0.0002}) - 5.0324)

Next Step Prepare to Evaluate

∴

ε i = \frac{1}{0.0001} \cdot (\ln (\frac{3}{0.0002}) - 5.0324)

Next Step Evaluate

∴

ε i = 40054.5752616546J

LAST Step Rounding Answer

∴

ε i = 40054.5753J

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Formula Elements

Variables

Functions

Energy of i-th State

Energy of i-th State is defined as the total quantity of energy present in a particular energy state.

Symbol: ε_i

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Energy of i-th State

Lagrange's Undetermined Multiplier 'β'

Lagrange's Undetermined Multiplier 'β' is denoted by 1/kT. Where, k= Boltzmann constant, T= temperature.

Symbol: β

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Lagrange's Undetermined Multiplier 'β'

Number of Degenerate States

Number of Degenerate States can be defined as the number of energy states that have the same energy.

Symbol: g

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Degenerate States

Number of particles in i-th State

Number of particles in i-th State can be defined as the total number of particles present in a particular energy state.

Symbol: n_i

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of particles in i-th State

Lagrange's Undetermined Multiplier 'α'

Lagrange's Undetermined Multiplier 'α' is denoted by μ/kT, Where μ= chemical potential; k= Boltzmann constant; T= temperature.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Lagrange's Undetermined Multiplier 'α'

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 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 Energy of I-th State for Maxwell-Boltzmann Statistics?

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics evaluator uses Energy of i-th State = 1/Lagrange's Undetermined Multiplier 'β'*(ln(Number of Degenerate States/Number of particles in i-th State)-Lagrange's Undetermined Multiplier 'α') to evaluate the Energy of i-th State, The Determination of Energy of I-th State for Maxwell-Boltzmann Statistics formula is defined as the amount of energy in a particular state. Energy of i-th State is denoted by ε_i symbol.

How to evaluate Determination of Energy of I-th State for Maxwell-Boltzmann Statistics using this online evaluator? To use this online evaluator for Determination of Energy of I-th State for Maxwell-Boltzmann Statistics, enter Lagrange's Undetermined Multiplier 'β' (β), Number of Degenerate States (g), Number of particles in i-th State (n_i) & Lagrange's Undetermined Multiplier 'α' (α) and hit the calculate button.

FAQs on Determination of Energy of I-th State for Maxwell-Boltzmann Statistics

What is the formula to find Determination of Energy of I-th State for Maxwell-Boltzmann Statistics?

The formula of Determination of Energy of I-th State for Maxwell-Boltzmann Statistics is expressed as Energy of i-th State = 1/Lagrange's Undetermined Multiplier 'β'*(ln(Number of Degenerate States/Number of particles in i-th State)-Lagrange's Undetermined Multiplier 'α'). Here is an example- 40054.58 = 1/0.00012*(ln(3/0.00016)-5.0324).

How to calculate Determination of Energy of I-th State for Maxwell-Boltzmann Statistics?

With Lagrange's Undetermined Multiplier 'β' (β), Number of Degenerate States (g), Number of particles in i-th State (n_i) & Lagrange's Undetermined Multiplier 'α' (α) we can find Determination of Energy of I-th State for Maxwell-Boltzmann Statistics using the formula - Energy of i-th State = 1/Lagrange's Undetermined Multiplier 'β'*(ln(Number of Degenerate States/Number of particles in i-th State)-Lagrange's Undetermined Multiplier 'α'). This formula also uses Natural Logarithm (ln) function(s).

Can the Determination of Energy of I-th State for Maxwell-Boltzmann Statistics be negative?

Yes, the Determination of Energy of I-th State for Maxwell-Boltzmann Statistics, measured in Energy can be negative.

Which unit is used to measure Determination of Energy of I-th State for Maxwell-Boltzmann Statistics?

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Determination of Energy of I-th State for Maxwell-Boltzmann Statistics can be measured.

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Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Formula

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Example

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Solution

Determination of Energy of I-th State for Maxwell-Boltzmann Statistics Formula Elements

Other formulas in Distinguishable Particles category

How to Evaluate Determination of Energy of I-th State for Maxwell-Boltzmann Statistics?

FAQs on Determination of Energy of I-th State for Maxwell-Boltzmann Statistics

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