Energy Density given Einstein Co-Efficients Calculator

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✖Frequency of Radiation refers to the number of oscillations or cycles of a wave that occur in a unit of time.ⓘ Frequency of Radiation [f_r]			+10% -10%
✖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%
✖Temperature is a measure of the average kinetic energy of the particles in a substance.ⓘ Temperature [T_o]			+10% -10%

✖Energy Density is the total amount of energy in a system per unit volume.ⓘ Energy Density given Einstein Co-Efficients [u]

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Energy Density given Einstein Co-Efficients

Formula

`"u" = (8*"[hP]"*"f"_{"r"}^3)/"[c]"^3*(1/(exp(("h"_{"p"}*"f"_{"r"})/("[BoltZ]"*"T"_{"o"}))-1))`

Example

`"3.9E^-42J/m³"=(8*"[hP]"*("57Hz")^3)/"[c]"^3*(1/(exp(("6.626E^-34"*"57Hz")/("[BoltZ]"*"293K"))-1))`

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Energy Density given Einstein Co-Efficients Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1))
u = (8*[hP]*f_r^3)/[c]^3*(1/(exp((h_p*f_r)/([BoltZ]*T_o))-1))
This formula uses 3 Constants, 1 Functions, 4 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
[c] - Light speed in vacuum Value Taken As 299792458.0

Functions Used

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

Variables Used

Energy Density - (Measured in Joule per Cubic Meter) - Energy Density is the total amount of energy in a system per unit volume.
Frequency of Radiation - (Measured in Hertz) - Frequency of Radiation refers to the number of oscillations or cycles of a wave that occur in a unit of time.
Planck's Constant - Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.
Temperature - (Measured in Kelvin) - Temperature is a measure of the average kinetic energy of the particles in a substance.

STEP 1: Convert Input(s) to Base Unit

Frequency of Radiation: 57 Hertz --> 57 Hertz No Conversion Required
Planck's Constant: 6.626E-34 --> No Conversion Required
Temperature: 293 Kelvin --> 293 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u = (8*[hP]*f_r^3)/[c]^3*(1/(exp((h_p*f_r)/([BoltZ]*T_o))-1)) --> (8*[hP]*57^3)/[c]^3*(1/(exp((6.626E-34*57)/([BoltZ]*293))-1))

Evaluating ... ...

u = 3.90241297636909E-42

STEP 3: Convert Result to Output's Unit

3.90241297636909E-42 Joule per Cubic Meter --> No Conversion Required

FINAL ANSWER

3.90241297636909E-42 ≈ 3.9E-42 Joule per Cubic Meter <-- Energy Density

(Calculation completed in 00.004 seconds)

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Created by banuprakash

Dayananda Sagar College of Engineering (DSCE), Bangalore

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Verified by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

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< 13 Photonics Devices Calculators

Saturation Current Density

Go Saturation Current Density = [Charge-e]*((Diffusion Coefficient of Hole)/Diffusion Length of Hole*Hole Concentration in n-Region+(Electron Diffusion Coefficient)/Diffusion Length of Electron*Electron Concentration in p-Region)

Spectral Radiant Emittance

Go Spectral Radiant Emittance = (2*pi*[hP]*[c]^3)/Wavelength of Visible Light^5*1/(exp(([hP]*[c])/(Wavelength of Visible Light*[BoltZ]*Absolute Temperature))-1)

Contact Potential Difference

Go Voltage Across PN Junction = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln((Acceptor Concentration*Donor Concentration)/(Intrinsic Carrier Concentration)^2)

Energy Density given Einstein Co-Efficients

Go Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1))

Proton Concentration under Unbalanced Condition

Go Proton Concentration = Intrinsic Electron Concentration*exp((Intrinsic Energy Level of Semiconductor-Quasi Fermi Level of Electrons)/([BoltZ]*Absolute Temperature))

Total Current Density

Go Total Current Density = Saturation Current Density*(exp(([Charge-e]*Voltage Across PN Junction)/([BoltZ]*Absolute Temperature))-1)

Net Phase Shift

Go Net Phase Shift = pi/Wavelength of Light*(Refractive Index)^3*Length of Fiber*Supply Voltage

Relative Population

Go Relative Population = exp(-([hP]*Relative Frequency)/([BoltZ]*Absolute Temperature))

Optical Power Radiated

Go Optical Power Radiated = Emissivity*[Stefan-BoltZ]*Area of Source*Temperature^4

Mode Number

Go Mode Number = (2*Length of Cavity*Refractive Index)/Photon Wavelength

Wavelength of Radiation in Vaccum

Go Wavelength of Wave = Apex Angle*(180/pi)*2*Single Pinhole

Wavelength of Output Light

Go Wavelength of Light = Refractive Index*Photon Wavelength

Length of Cavity

Go Length of Cavity = (Photon Wavelength*Mode Number)/2

Energy Density given Einstein Co-Efficients Formula

Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1))
u = (8*[hP]*f_r^3)/[c]^3*(1/(exp((h_p*f_r)/([BoltZ]*T_o))-1))

Why is energy density important?

Energy density is crucial in various fields, such as energy storage, transportation, and nutrition. High energy density materials are sought after for efficient energy storage and portable power sources.

How to Calculate Energy Density given Einstein Co-Efficients?

Energy Density given Einstein Co-Efficients calculator uses Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1)) to calculate 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 calculate Energy Density given Einstein Co-Efficients using this online calculator? To use this online calculator 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. Here is how the Energy Density given Einstein Co-Efficients calculation can be explained with given input values -> 3.9E-42 = (8*[hP]*57^3)/[c]^3*(1/(exp((6.626E-34*57)/([BoltZ]*293))-1)).

FAQ

What is Energy Density given Einstein Co-Efficients?

The Energy Density given Einstein Co-Efficients formula is defined as the total amount of energy in a system per unit volume and is represented as u = (8*[hP]*f_r^3)/[c]^3*(1/(exp((h_p*f_r)/([BoltZ]*T_o))-1)) or Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1)). Frequency of Radiation refers to the number of oscillations or cycles of a wave that occur in a unit of time, Planck's Constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency & Temperature is a measure of the average kinetic energy of the particles in a substance.

How to calculate Energy Density given Einstein Co-Efficients?

The Energy Density given Einstein Co-Efficients formula is defined as the total amount of energy in a system per unit volume is calculated using Energy Density = (8*[hP]*Frequency of Radiation^3)/[c]^3*(1/(exp((Planck's Constant*Frequency of Radiation)/([BoltZ]*Temperature))-1)). To calculate Energy Density given Einstein Co-Efficients, you need Frequency of Radiation (f_r), Planck's Constant (h_p) & Temperature (T_o). With our tool, you need to enter the respective value for Frequency of Radiation, Planck's Constant & Temperature 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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