Temperature dependent diffusion coefficient Calculator

✖Pre-exponential factor to calculate diffusion coefficient.ⓘ Pre-exponential factor [D₀]			+10% -10%
✖Activation energy for diffusion that is energy required to produce the diffusive motion of an atom.ⓘ Activation energy for diffusion [Q_d]			+10% -10%
✖Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joulekelvin−1mole−1.ⓘ Universal Gas Constant [R]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖Diffusion coefficient is the proportionality factor D in Fick's law .ⓘ Temperature dependent diffusion coefficient [D]

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Formula

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Temperature dependent diffusion coefficient

Formula

`"D" = "D"_{"0"}*e^(-"Q"_{"d"}/("R"*"T"))`

Example

`"0.0001m²/s"="0.0001m²/s"*e^(-"1.31eV"/("8.314"*"85K"))`

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Temperature dependent diffusion coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature))
D = D₀*e^(-Q_d/(R*T))
This formula uses 1 Constants, 5 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

Diffusion Coefficient - (Measured in Square Meter Per Second) - Diffusion coefficient is the proportionality factor D in Fick's law .
Pre-exponential factor - (Measured in Square Meter Per Second) - Pre-exponential factor to calculate diffusion coefficient.
Activation energy for diffusion - (Measured in Joule) - Activation energy for diffusion that is energy required to produce the diffusive motion of an atom.
Universal Gas Constant - Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Pre-exponential factor: 0.0001 Square Meter Per Second --> 0.0001 Square Meter Per Second No Conversion Required
Activation energy for diffusion: 1.31 Electron-Volt --> 2.09885230230001E-19 Joule (Check conversion here)
Universal Gas Constant: 8.314 --> No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = D₀*e^(-Q_d/(R*T)) --> 0.0001*e^(-2.09885230230001E-19/(8.314*85))

Evaluating ... ...

D = 0.0001

STEP 3: Convert Result to Output's Unit

0.0001 Square Meter Per Second --> No Conversion Required

FINAL ANSWER

0.0001 Square Meter Per Second <-- Diffusion Coefficient

(Calculation completed in 00.004 seconds)

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< 9 Composition and Diffusion Calculators

Atom percent to mass percent

Go Mass Percent of First Element = Atomic percent of first element*Atomic mass of first element*100/(Atomic percent of first element*Atomic mass of first element+(100-Atomic percent of first element)*Atomic mass of second element)

Atom percent

Go Atomic percent of first element = 100*Mass Percent of First Element*Atomic mass of second element/(Mass Percent of First Element*Atomic mass of second element+(100-Mass Percent of First Element)*Atomic mass of first element)

Non-steady state diffusion

Go Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time))))

Volume percent to mass percent

Go Mass percent of first phase = Volume percent of first phase*Density of the first phase*100/(Volume percent of first phase*Density of the first phase+(100-Volume percent of first phase)*Density of the second phase)

Mass percent to volume percent

Go Volume percent of first phase = Mass percent of first phase*Density of the second phase*100/(Mass percent of first phase*Density of the second phase+(100-Mass percent of first phase)*Density of the first phase)

Entropy of mixing

Go Entropy of mixing = 8.314*(Mole fraction of element A*ln(Mole fraction of element A)+(1-Mole fraction of element A)*ln(1-Mole fraction of element A))

Equilibrium Vacancy Concentration

Go Number of vacancies = Number of atomic sites*exp(-Activation energy for vacancy formation/([BoltZ]*Temperature))

Temperature dependent diffusion coefficient

Go Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature))

Diffusion Flux

Go Diffusion flux = Diffusion Coefficient*(Concentration difference/Distance)

Temperature dependent diffusion coefficient Formula

Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature))
D = D₀*e^(-Q_d/(R*T))

What is mass diffusivity?

Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species. Diffusivity is encountered in Fick's law and numerous other equations of physical chemistry. The diffusivity is generally prescribed for a given pair of species and pairwise for a multi-species system.

How to Calculate Temperature dependent diffusion coefficient?

Temperature dependent diffusion coefficient calculator uses Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature)) to calculate the Diffusion Coefficient, Temperature dependent diffusion coefficient gives the dependency of the diffusion coefficient of solids, liquids, and gases on temperature. Diffusion Coefficient is denoted by D symbol.

How to calculate Temperature dependent diffusion coefficient using this online calculator? To use this online calculator for Temperature dependent diffusion coefficient, enter Pre-exponential factor (D₀), Activation energy for diffusion (Q_d), Universal Gas Constant (R) & Temperature (T) and hit the calculate button. Here is how the Temperature dependent diffusion coefficient calculation can be explained with given input values -> 0.0001 = 0.0001*e^(-2.09885230230001E-19/(8.314*85)).

FAQ

What is Temperature dependent diffusion coefficient?

Temperature dependent diffusion coefficient gives the dependency of the diffusion coefficient of solids, liquids, and gases on temperature and is represented as D = D₀*e^(-Q_d/(R*T)) or Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature)). Pre-exponential factor to calculate diffusion coefficient, Activation energy for diffusion that is energy required to produce the diffusive motion of an atom, Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1 & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Temperature dependent diffusion coefficient?

Temperature dependent diffusion coefficient gives the dependency of the diffusion coefficient of solids, liquids, and gases on temperature is calculated using Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature)). To calculate Temperature dependent diffusion coefficient, you need Pre-exponential factor (D₀), Activation energy for diffusion (Q_d), Universal Gas Constant (R) & Temperature (T). With our tool, you need to enter the respective value for Pre-exponential factor, Activation energy for diffusion, Universal Gas 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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