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Debye Temperature Formula

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Debye temperature is the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties. Check FAQs

θ D = ([hP] \cdot \frac{v a}{[BoltZ]}) \cdot \frac{{(0.75 \cdot π \cdot NV)}^{1}}{3}

θ_D - Debye Temperature?v_a - Speed of sound in solid?NV - Number of atoms per unit volume for the solid?[hP] - Planck constant?[BoltZ] - Boltzmann constant?π - Archimedes' constant?

Debye Temperature Example

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Here is how the Debye Temperature equation looks like with Values.

Here is how the Debye Temperature equation looks like with Units.

Here is how the Debye Temperature equation looks like.

1.4E-6 = (6.6E-34 \cdot \frac{6000}{1.4E-23}) \cdot \frac{{(0.75 \cdot 3.1416 \cdot 6.025)}^{1}}{3}

1.4E-6K = (6.6E-34 \cdot \frac{6000m/s}{1.4E-23J/K}) \cdot \frac{{(0.75 \cdot 3.1416 \cdot 6.025)}^{1}}{3}

1.4E-6 = (6.6E-34 \cdot \frac{6000}{1.4E-23}) \cdot \frac{{(0.75 \cdot 3.1416 \cdot 6.025)}^{1}}{3}

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Debye Temperature Solution

Follow our step by step solution on how to calculate Debye Temperature?

FIRST Step Consider the formula

θ D = ([hP] \cdot \frac{v a}{[BoltZ]}) \cdot \frac{{(0.75 \cdot π \cdot NV)}^{1}}{3}

Next Step Substitute values of Variables

∴

θ D = ([hP] \cdot \frac{6000m/s}{[BoltZ]}) \cdot \frac{{(0.75 \cdot π \cdot 6.025)}^{1}}{3}

Next Step Substitute values of Constants

∴

θ D = (6.6E-34 \cdot \frac{6000m/s}{1.4E-23J/K}) \cdot \frac{{(0.75 \cdot 3.1416 \cdot 6.025)}^{1}}{3}

Next Step Prepare to Evaluate

∴

θ D = (6.6E-34 \cdot \frac{6000}{1.4E-23}) \cdot \frac{{(0.75 \cdot 3.1416 \cdot 6.025)}^{1}}{3}

Next Step Evaluate

∴

θ D = 1.36260843653758E-06K

LAST Step Rounding Answer

∴

θ D = 1.4E-6K

Debye Temperature Formula Elements

Variables

Constants

Debye Temperature

Debye temperature is the temperature of a crystal's highest normal mode of vibration, and it correlates the elastic properties with the thermodynamic properties.

Symbol: θ_D

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Debye Temperature

Speed of sound in solid

The speed of sound in solid is the measure of the sound that travels through any solid.

Symbol: v_a

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Speed of sound in 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.

Symbol: NV

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of atoms per unit volume for the solid

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

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

How to Evaluate Debye Temperature?

Debye Temperature evaluator 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 evaluate 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 evaluate Debye Temperature using this online evaluator? To use this online evaluator 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.

FAQs on Debye Temperature

What is the formula to find Debye Temperature?

The formula of Debye Temperature is expressed as Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3. Here is an example- 1.4E-6 = ([hP]*6000/[BoltZ])*(0.75*pi*6.025)^1/3.

How to calculate Debye Temperature?

With Speed of sound in solid (v_a) & Number of atoms per unit volume for the solid (NV) we can find Debye Temperature using the formula - Debye Temperature = ([hP]*Speed of sound in solid/[BoltZ])*(0.75*pi*Number of atoms per unit volume for the solid)^1/3. This formula also uses Planck constant, Boltzmann constant, Archimedes' constant .

Can the Debye Temperature be negative?

No, the Debye Temperature, measured in Temperature cannot be negative.

Which unit is used to measure Debye Temperature?

Debye Temperature is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Debye Temperature can be measured.

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Debye Temperature Formula

Debye Temperature Example

Debye Temperature Solution

Debye Temperature Formula Elements

How to Evaluate Debye Temperature?

FAQs on Debye Temperature

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