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Determination of Critical Temperature in Bose-Einstein Statistics Formula

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Critical Temperature can be defined as the minimum temperature at which the limiting value z' =1. Check FAQs

T 0 = \frac{{h p}^{2}}{2 \cdot π \cdot m \cdot [BoltZ]} \cdot {(\frac{ρ}{2.612})}^{\frac{2}{3}}

T₀ - Critical Temperature?h_p - Planck's Constant?m - Mass?ρ - Mass Density?[BoltZ] - Boltzmann constant?π - Archimedes' constant?

Determination of Critical Temperature in Bose-Einstein Statistics Example

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Here is how the Determination of Critical Temperature in Bose-Einstein Statistics equation looks like with Values.

Here is how the Determination of Critical Temperature in Bose-Einstein Statistics equation looks like with Units.

Here is how the Determination of Critical Temperature in Bose-Einstein Statistics equation looks like.

141.7578 = \frac{{6.6E-34}^{2}}{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23} \cdot {(\frac{5.3E+31}{2.612})}^{\frac{2}{3}}

141.7578K = \frac{{6.6E-34}^{2}}{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K} \cdot {(\frac{5.3E+31kg/m³}{2.612})}^{\frac{2}{3}}

141.7578 = \frac{{6.6E-34}^{2}}{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23} \cdot {(\frac{5.3E+31}{2.612})}^{\frac{2}{3}}

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Determination of Critical Temperature in Bose-Einstein Statistics Solution

Follow our step by step solution on how to calculate Determination of Critical Temperature in Bose-Einstein Statistics?

FIRST Step Consider the formula

T 0 = \frac{{h p}^{2}}{2 \cdot π \cdot m \cdot [BoltZ]} \cdot {(\frac{ρ}{2.612})}^{\frac{2}{3}}

Next Step Substitute values of Variables

∴

T 0 = \frac{{6.6E-34}^{2}}{2 \cdot π \cdot 2.7E-26kg \cdot [BoltZ]} \cdot {(\frac{5.3E+31kg/m³}{2.612})}^{\frac{2}{3}}

Next Step Substitute values of Constants

∴

T 0 = \frac{{6.6E-34}^{2}}{2 \cdot 3.1416 \cdot 2.7E-26kg \cdot 1.4E-23J/K} \cdot {(\frac{5.3E+31kg/m³}{2.612})}^{\frac{2}{3}}

Next Step Prepare to Evaluate

∴

T 0 = \frac{{6.6E-34}^{2}}{2 \cdot 3.1416 \cdot 2.7E-26 \cdot 1.4E-23} \cdot {(\frac{5.3E+31}{2.612})}^{\frac{2}{3}}

Next Step Evaluate

∴

T 0 = 141.757786645324K

LAST Step Rounding Answer

∴

T 0 = 141.7578K

Determination of Critical Temperature in Bose-Einstein Statistics Formula Elements

Variables

Constants

Critical Temperature

Critical Temperature can be defined as the minimum temperature at which the limiting value z' =1.

Symbol: T₀

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Critical Temperature

Planck's Constant

Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.

Symbol: h_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Planck's Constant

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

Mass Density

Mass Density is a representation of the amount of mass (or the number of particles) of a substance, material or object in relation to the space it occupies.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value can be positive or negative.

Formulas to find Mass Density

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

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 in Indistinguishable Particles category

Go Mathematical Probability of Occurrence of Distribution

ρ = \frac{W}{W tot}

Go Boltzmann-Planck Equation

S = [BoltZ] \cdot \ln (W)

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

A = - N A \cdot [BoltZ] \cdot T \cdot (\ln (\frac{q}{N A}) + 1)

Go Determination of Gibbs Free energy using Molecular PF for Indistinguishable Particles

G = - N A \cdot [BoltZ] \cdot T \cdot \ln (\frac{q}{N A})

How to Evaluate Determination of Critical Temperature in Bose-Einstein Statistics?

Determination of Critical Temperature in Bose-Einstein Statistics evaluator uses Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3) to evaluate the Critical Temperature, The Determination of Critical Temperature in Bose-Einstein Statistics formula is very close to absolute zero, which is −273.15 °C or −459.67 °F or 0 K. Critical Temperature is denoted by T₀ symbol.

How to evaluate Determination of Critical Temperature in Bose-Einstein Statistics using this online evaluator? To use this online evaluator for Determination of Critical Temperature in Bose-Einstein Statistics, enter Planck's Constant (h_p), Mass (m) & Mass Density (ρ) and hit the calculate button.

FAQs on Determination of Critical Temperature in Bose-Einstein Statistics

What is the formula to find Determination of Critical Temperature in Bose-Einstein Statistics?

The formula of Determination of Critical Temperature in Bose-Einstein Statistics is expressed as Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3). Here is an example- 2.3E-19 = 6.626E-34^2/(2*pi*2.656E-26*[BoltZ])*(5.3E+31/2.612)^(2/3).

How to calculate Determination of Critical Temperature in Bose-Einstein Statistics?

With Planck's Constant (h_p), Mass (m) & Mass Density (ρ) we can find Determination of Critical Temperature in Bose-Einstein Statistics using the formula - Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3). This formula also uses Boltzmann constant, Archimedes' constant .

Can the Determination of Critical Temperature in Bose-Einstein Statistics be negative?

Yes, the Determination of Critical Temperature in Bose-Einstein Statistics, measured in Temperature can be negative.

Which unit is used to measure Determination of Critical Temperature in Bose-Einstein Statistics?

Determination of Critical Temperature in Bose-Einstein Statistics is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Determination of Critical Temperature in Bose-Einstein Statistics can be measured.

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Determination of Critical Temperature in Bose-Einstein Statistics Formula

Determination of Critical Temperature in Bose-Einstein Statistics Example

Determination of Critical Temperature in Bose-Einstein Statistics Solution

Determination of Critical Temperature in Bose-Einstein Statistics Formula Elements

Other formulas in Indistinguishable Particles category

How to Evaluate Determination of Critical Temperature in Bose-Einstein Statistics?

FAQs on Determination of Critical Temperature in Bose-Einstein Statistics

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