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Energy Density given Einstein Co-Efficients Formula

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Energy Density is the total amount of energy in a system per unit volume. Check FAQs

u = \frac{8 \cdot [hP] \cdot {f r}^{3}}{{[c]}^{3}} \cdot (\frac{1}{\exp (\frac{h p \cdot f r}{[BoltZ] \cdot T o}) - 1})

u - Energy Density?f_r - Frequency of Radiation?h_p - Planck's Constant?T_o - Temperature?[hP] - Planck constant?[c] - Light speed in vacuum?[BoltZ] - Boltzmann constant?

Energy Density given Einstein Co-Efficients Example

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Here is how the Energy Density given Einstein Co-Efficients equation looks like with Values.

Here is how the Energy Density given Einstein Co-Efficients equation looks like with Units.

Here is how the Energy Density given Einstein Co-Efficients equation looks like.

3.9E-42 = \frac{8 \cdot 6.6E-34 \cdot 57^{3}}{{3E+8}^{3}} \cdot (\frac{1}{\exp (\frac{6.6E-34 \cdot 57}{1.4E-23 \cdot 293}) - 1})

3.9E-42J/m³ = \frac{8 \cdot 6.6E-34 \cdot {57Hz}^{3}}{{3E+8m/s}^{3}} \cdot (\frac{1}{\exp (\frac{6.6E-34 \cdot 57Hz}{1.4E-23J/K \cdot 293K}) - 1})

3.9E-42 = \frac{8 \cdot 6.6E-34 \cdot 57^{3}}{{3E+8}^{3}} \cdot (\frac{1}{\exp (\frac{6.6E-34 \cdot 57}{1.4E-23 \cdot 293}) - 1})

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Energy Density given Einstein Co-Efficients Solution

Follow our step by step solution on how to calculate Energy Density given Einstein Co-Efficients?

FIRST Step Consider the formula

u = \frac{8 \cdot [hP] \cdot {f r}^{3}}{{[c]}^{3}} \cdot (\frac{1}{\exp (\frac{h p \cdot f r}{[BoltZ] \cdot T o}) - 1})

Next Step Substitute values of Variables

∴

u = \frac{8 \cdot [hP] \cdot {57Hz}^{3}}{{[c]}^{3}} \cdot (\frac{1}{\exp (\frac{6.6E-34 \cdot 57Hz}{[BoltZ] \cdot 293K}) - 1})

Next Step Substitute values of Constants

∴

u = \frac{8 \cdot 6.6E-34 \cdot {57Hz}^{3}}{{3E+8m/s}^{3}} \cdot (\frac{1}{\exp (\frac{6.6E-34 \cdot 57Hz}{1.4E-23J/K \cdot 293K}) - 1})

Next Step Prepare to Evaluate

∴

u = \frac{8 \cdot 6.6E-34 \cdot 57^{3}}{{3E+8}^{3}} \cdot (\frac{1}{\exp (\frac{6.6E-34 \cdot 57}{1.4E-23 \cdot 293}) - 1})

Next Step Evaluate

∴

u = 3.90241297636909E-42J/m³

LAST Step Rounding Answer

∴

u = 3.9E-42J/m³

Energy Density given Einstein Co-Efficients Formula Elements

Variables

Constants

Functions

Energy Density

Energy Density is the total amount of energy in a system per unit volume.

Symbol: u

Measurement: Energy DensityUnit: J/m³

Note: Value should be greater than 0.

Formulas to find Energy Density

Frequency of Radiation

Frequency of Radiation refers to the number of oscillations or cycles of a wave that occur in a unit of time.

Symbol: f_r

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Frequency of Radiation

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

Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance.

Symbol: T_o

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature

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

Light speed in vacuum

Light speed in vacuum is a fundamental physical constant representing the speed at which light propagates through a vacuum.

Symbol: [c]

Value: 299792458.0 m/s

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

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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Go Optical Power Radiated

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Go Net Phase Shift

ΔΦ = \frac{π}{λ o} \cdot {(n ri)}^{3} \cdot r \cdot V cc

Go Length of Cavity

L c = \frac{λ \cdot m}{2}

Go Mode Number

m = \frac{2 \cdot L c \cdot n ri}{λ}

How to Evaluate Energy Density given Einstein Co-Efficients?

Energy Density given Einstein Co-Efficients evaluator uses Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1)) to evaluate the Energy Density, The Energy Density given Einstein Co-Efficients formula is defined as the total amount of energy in a system per unit volume. Energy Density is denoted by u symbol.

How to evaluate Energy Density given Einstein Co-Efficients using this online evaluator? To use this online evaluator for Energy Density given Einstein Co-Efficients, enter Frequency of Radiation (f_r), Planck's Constant (h_p) & Temperature (T_o) and hit the calculate button.

FAQs on Energy Density given Einstein Co-Efficients

What is the formula to find Energy Density given Einstein Co-Efficients?

The formula of Energy Density given Einstein Co-Efficients is expressed as Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1)). Here is an example- 3.9E-42 = (8*[hP]*57^3)/[c]^3*(1/(exp((6.626E-34*57)/([BoltZ]*293))-1)).

How to calculate Energy Density given Einstein Co-Efficients?

With Frequency of Radiation (f_r), Planck's Constant (h_p) & Temperature (T_o) we can find Energy Density given Einstein Co-Efficients using the formula - Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1)). This formula also uses Planck constant, Light speed in vacuum, Boltzmann constant and Exponential Growth (exp) function(s).

Can the Energy Density given Einstein Co-Efficients be negative?

No, the Energy Density given Einstein Co-Efficients, measured in Energy Density cannot be negative.

Which unit is used to measure Energy Density given Einstein Co-Efficients?

Energy Density given Einstein Co-Efficients is usually measured using the Joule per Cubic Meter[J/m³] for Energy Density. Kilojoule per Cubic Meter[J/m³], Megajoule per Cubic Meter[J/m³] are the few other units in which Energy Density given Einstein Co-Efficients can be measured.

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Energy Density given Einstein Co-Efficients Formula

Energy Density given Einstein Co-Efficients Example

Energy Density given Einstein Co-Efficients Solution

Energy Density given Einstein Co-Efficients Formula Elements

Other formulas in Photonics Devices category

How to Evaluate Energy Density given Einstein Co-Efficients?

FAQs on Energy Density given Einstein Co-Efficients

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