Debye Temperature Calculator

✖The speed of sound in solid is the measure of the sound that travels through any solid.ⓘ Speed of sound in solid [v_a]			+10% -10%
✖Number of atoms per unit volume for the solid states the number of atoms occupying the space present in any solid body.ⓘ Number of atoms per unit volume for the solid [NV]			+10% -10%

✖Debye temperature is the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties.ⓘ Debye Temperature [θ_D]

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Formula

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Debye Temperature

Formula

`"θ"_{"D"} = ("[hP]"*"v"_{"a"}/"[BoltZ]")*(0.75*pi*"NV")^1/3`

Example

`"1.4E^-6K"=("[hP]"*"6000m/s"/"[BoltZ]")*(0.75*pi*"6.025")^1/3`

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Debye Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3
θ_D = ([hP]*v_a/[BoltZ])*(0.75*pi*NV)^1/3
This formula uses 3 Constants, 3 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Debye Temperature - (Measured in Kelvin) - Debye temperature is the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties.
Speed of sound in solid - (Measured in Meter per Second) - The speed of sound in solid is the measure of the sound that travels through any solid.
Number of atoms per unit volume for the solid - Number of atoms per unit volume for the solid states the number of atoms occupying the space present in any solid body.

STEP 1: Convert Input(s) to Base Unit

Speed of sound in solid: 6000 Meter per Second --> 6000 Meter per Second No Conversion Required
Number of atoms per unit volume for the solid: 6.025 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_D = ([hP]*v_a/[BoltZ])*(0.75*pi*NV)^1/3 --> ([hP]*6000/[BoltZ])*(0.75*pi*6.025)^1/3

Evaluating ... ...

θ_D = 1.36260843653758E-06

STEP 3: Convert Result to Output's Unit

1.36260843653758E-06 Kelvin --> No Conversion Required

FINAL ANSWER

1.36260843653758E-06 ≈ 1.4E-6 Kelvin <-- Debye Temperature

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

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< 1 Cryogenic Systems Calculators

Debye Temperature

Go Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3

Debye Temperature Formula

Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3
θ_D = ([hP]*v_a/[BoltZ])*(0.75*pi*NV)^1/3

What is Debye temperature?

The Debye temperature ΘD is the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties such as phonons, thermal expansion, thermal conductivity, specific heat, and lattice enthalpy..

How to Calculate Debye Temperature?

Debye Temperature calculator uses Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3 to calculate the Debye Temperature, The Debye Temperature formula is defined as the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties such as phonons, thermal expansion, thermal conductivity, specific heat, and lattice enthalpy. Debye Temperature is denoted by θ_D symbol.

How to calculate Debye Temperature using this online calculator? To use this online calculator for Debye Temperature, enter Speed of sound in solid (v_a) & Number of atoms per unit volume for the solid (NV) and hit the calculate button. Here is how the Debye Temperature calculation can be explained with given input values -> 1.4E-6 = ([hP]*6000/[BoltZ])*(0.75*pi*6.025)^1/3.

FAQ

What is Debye Temperature?

The Debye Temperature formula is defined as the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties such as phonons, thermal expansion, thermal conductivity, specific heat, and lattice enthalpy and is represented as θ_D = ([hP]*v_a/[BoltZ])*(0.75*pi*NV)^1/3 or Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3. The speed of sound in solid is the measure of the sound that travels through any solid & Number of atoms per unit volume for the solid states the number of atoms occupying the space present in any solid body.

How to calculate Debye Temperature?

The Debye Temperature formula is defined as the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties such as phonons, thermal expansion, thermal conductivity, specific heat, and lattice enthalpy is calculated using Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3. To calculate Debye Temperature, you need Speed of sound in solid (v_a) & Number of atoms per unit volume for the solid (NV). With our tool, you need to enter the respective value for Speed of sound in solid & Number of atoms per unit volume for the solid 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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