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Determination of Critical Temperature in Bose-Einstein Statistics Calculator

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Indistinguishable Particles Distinguishable Particles

✖Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.ⓘ Planck's Constant [h_p]			+10% -10%
✖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.ⓘ Mass [m]			+10% -10%
✖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.ⓘ Mass Density [ρ]			+10% -10%

✖Critical Temperature can be defined as the minimum temperature at which the limiting value z' =1.ⓘ Determination of Critical Temperature in Bose-Einstein Statistics [T₀]

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Determination of Critical Temperature in Bose-Einstein Statistics Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3)
T₀ = h_p^2/(2*pi*m*[BoltZ])*(ρ/2.612)^(2/3)
This formula uses 2 Constants, 4 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Critical Temperature - (Measured in Kelvin) - Critical Temperature can be defined as the minimum temperature at which the limiting value z' =1.
Planck's Constant - Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.
Mass - (Measured in Kilogram) - 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.
Mass Density - (Measured in Kilogram per Cubic Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Planck's Constant: 6.626E-34 --> No Conversion Required
Mass: 2.656E-26 Kilogram --> 2.656E-26 Kilogram No Conversion Required
Mass Density: 5.3E+31 Kilogram per Cubic Meter --> 5.3E+31 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T₀ = h_p^2/(2*pi*m*[BoltZ])*(ρ/2.612)^(2/3) --> 6.626E-34^2/(2*pi*2.656E-26*[BoltZ])*(5.3E+31/2.612)^(2/3)

Evaluating ... ...

T₀ = 141.757786645324

STEP 3: Convert Result to Output's Unit

141.757786645324 Kelvin --> No Conversion Required

FINAL ANSWER

141.757786645324 ≈ 141.7578 Kelvin <-- Critical Temperature

(Calculation completed in 00.004 seconds)

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Determination of Critical Temperature in Bose-Einstein Statistics Formula

LaTeX Go

Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3)
T₀ = h_p^2/(2*pi*m*[BoltZ])*(ρ/2.612)^(2/3)

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 Determination of Critical Temperature in Bose-Einstein Statistics?

Determination of Critical Temperature in Bose-Einstein Statistics calculator uses Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3) to calculate 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 calculate Determination of Critical Temperature in Bose-Einstein Statistics using this online calculator? To use this online calculator 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. Here is how the Determination of Critical Temperature in Bose-Einstein Statistics calculation can be explained with given input values -> 2.3E-19 = 6.626E-34^2/(2*pi*2.656E-26*[BoltZ])*(5.3E+31/2.612)^(2/3).

FAQ

What is Determination of Critical Temperature in Bose-Einstein Statistics?

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 and is represented as T₀ = h_p^2/(2*pi*m*[BoltZ])*(ρ/2.612)^(2/3) or Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3). Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency, 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 & 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.

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

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 is calculated using Critical Temperature = Planck's Constant^2/(2*pi*Mass*[BoltZ])*(Mass Density/2.612)^(2/3). To calculate Determination of Critical Temperature in Bose-Einstein Statistics, you need Planck's Constant (h_p), Mass (m) & Mass Density (ρ). With our tool, you need to enter the respective value for Planck's Constant, Mass & Mass Density 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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