Monochromatic Transmissivity Calculator

✖Monochromatic Absorption Coefficient is defined as the proportionality constant where thickness of the gas layer and the intensity of radiation are proportional.ⓘ Monochromatic Absorption Coefficient [α_λ]			+10% -10%
✖Distance is the length across which the absorption of radiation beam is taking place.ⓘ Distance [x]			+10% -10%

✖Monochromatic Transmissivity is the fraction of incident radiation beam transmitted through the body.ⓘ Monochromatic Transmissivity [𝜏_λ]

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Formula

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Monochromatic Transmissivity

Formula

`"𝜏"_{"λ"} = exp(-("α"_{"λ"}*"x"))`

Example

`"0.693919"=exp(-("0.42"*"0.87m"))`

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Monochromatic Transmissivity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance))
𝜏_λ = exp(-(α_λ*x))
This formula uses 1 Functions, 3 Variables

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

Monochromatic Transmissivity - Monochromatic Transmissivity is the fraction of incident radiation beam transmitted through the body.
Monochromatic Absorption Coefficient - Monochromatic Absorption Coefficient is defined as the proportionality constant where thickness of the gas layer and the intensity of radiation are proportional.
Distance - (Measured in Meter) - Distance is the length across which the absorption of radiation beam is taking place.

STEP 1: Convert Input(s) to Base Unit

Monochromatic Absorption Coefficient: 0.42 --> No Conversion Required
Distance: 0.87 Meter --> 0.87 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏_λ = exp(-(α_λ*x)) --> exp(-(0.42*0.87))

Evaluating ... ...

𝜏_λ = 0.693919027745956

STEP 3: Convert Result to Output's Unit

0.693919027745956 --> No Conversion Required

FINAL ANSWER

0.693919027745956 ≈ 0.693919 <-- Monochromatic Transmissivity

(Calculation completed in 00.004 seconds)

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Created by Ayush gupta

University School of Chemical Technology-USCT (GGSIPU), New Delhi

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Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< 5 Gas Radiation Calculators

Radiation Intensity at given Distance using Beer's Law

Go Radiation Intensity at Distance x = Initial Radiation Intensity*exp(-(Monochromatic Absorption Coefficient*Distance))

Initial Radiation Intensity

Go Initial Radiation Intensity = Radiation Intensity at Distance x/exp(-(Monochromatic Absorption Coefficient*Distance))

Monochromatic Transmissivity

Go Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance))

Monochromatic Absorption Coefficient if Gas is Non-Reflecting

Go Monochromatic Absorption Coefficient = 1-Monochromatic Transmissivity

Monochromatic Transmissivity if Gas is Non Reflecting

Go Monochromatic Transmissivity = 1-Monochromatic Absorption Coefficient

< 21 Important Formulas in Gas Radiation, Radiation Exchange with Specular Surfaces & more Special Cases Calculators

Net Heat Lost by Surface given Diffuse Radiosity

Go Heat Transfer = ((Emissivity*Area)/(Diffuse Component of Reflectivity))*((Emissive Power of Blackbody*(Emissivity+Diffuse Component of Reflectivity))-Diffuse Radiosity)

Transmissivity of Transparent Medium given Radiosity and Shape Factor

Go Transmissivity of Transparent Medium = Radiation Heat Transfer/(Surface Area of Body 1*Radiation Shape Factor 12*(Radiosity of 1st Body-Radiosity of 2nd Body))

Net Heat Exchange in Transmission Process

Go Radiation Heat Transfer = Surface Area of Body 1*Radiation Shape Factor 12*Transmissivity of Transparent Medium*(Radiosity of 1st Body-Radiosity of 2nd Body)

Diffuse Radiation Exchange from Surface 1 to Surface 2

Go Heat Transfer from Surface 1 to 2 = (Diffuse Radiosity for Surface 1*Surface Area of Body 1*Radiation Shape Factor 12)*(1-Specular Component of Reflectivity of Surface 2)

Diffuse Radiation Exchange from Surface 2 to Surface 1

Go Heat Transfer from Surface 2 to 1 = Diffuse Radiosity for Surface 2*Surface Area of Body 2*Radiation Shape Factor 21*(1-Specular Component of Reflectivity of Surface 1)

Energy Leaving Surface 1 that is Transmitted through Medium

Go Energy Leaving Surface = Radiosity of 1st Body*Surface Area of Body 1*Radiation Shape Factor 12*Transmissivity of Transparent Medium

Net Heat Lost by Surface

Go Heat Transfer = Area*((Emissivity*Emissive Power of Blackbody)-(Absorptivity*Irradiation))

Radiation Intensity at given Distance using Beer's Law

Go Radiation Intensity at Distance x = Initial Radiation Intensity*exp(-(Monochromatic Absorption Coefficient*Distance))

Initial Radiation Intensity

Go Initial Radiation Intensity = Radiation Intensity at Distance x/exp(-(Monochromatic Absorption Coefficient*Distance))

Diffuse Radiosity

Go Diffuse Radiosity = ((Emissivity*Emissive Power of Blackbody)+(Diffuse Component of Reflectivity*Irradiation))

Direct Diffuse Radiation from Surface 2 to Surface 1

Go Heat Transfer from Surface 2 to 1 = Surface Area of Body 2*Radiation Shape Factor 21*Radiosity of 2nd Body

Monochromatic Transmissivity

Go Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance))

Emissive Power of Blackbody through Medium given Emissivity of Medium

Go Emissive Power of Blackbody through Medium = Radiosity for Transparent Medium/Emissivity of Medium

Emissivity of Medium given Emissive Power of Blackbody through Medium

Go Emissivity of Medium = Radiosity for Transparent Medium/Emissive Power of Blackbody through Medium

Energy Emitted by Medium

Go Radiosity for Transparent Medium = Emissivity of Medium*Emissive Power of Blackbody through Medium

Temperature of Medium given Emissive Power of Blackbody

Go Temperature of Medium = (Emissive Power of Blackbody through Medium/[Stefan-BoltZ])^(1/4)

Transmissivity given Specular and Diffuse Component

Go Transmissivity = (Specular Component of Transmissivity+Diffuse Component of Transmissivity)

Emissive Power of Blackbody through Medium

Go Emissive Power of Blackbody through Medium = [Stefan-BoltZ]*(Temperature of Medium^4)

Reflectivity given Specular and Diffuse Component

Go Reflectivity = Specular Component of Reflectivity+Diffuse Component of Reflectivity

Monochromatic Absorption Coefficient if Gas is Non-Reflecting

Go Monochromatic Absorption Coefficient = 1-Monochromatic Transmissivity

Monochromatic Transmissivity if Gas is Non Reflecting

Go Monochromatic Transmissivity = 1-Monochromatic Absorption Coefficient

Monochromatic Transmissivity Formula

Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance))
𝜏_λ = exp(-(α_λ*x))

What is Radiation?

Radiation is energy that comes from a source and travels through space at the speed of light. This energy has an electric field and a magnetic field associated with it, and has wave-like properties. You could also call radiation “electromagnetic waves”.

What is Emissivity?

Emissivity is defined as the ratio of the energy radiated from a material's surface to that radiated from a perfect emitter, known as a blackbody, at the same temperature and wavelength and under the same viewing conditions. It is a dimensionless number between 0 (for a perfect reflector) and 1 (for a perfect emitter).

How to Calculate Monochromatic Transmissivity?

Monochromatic Transmissivity calculator uses Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance)) to calculate the Monochromatic Transmissivity, The Monochromatic Transmissivity formula is defined as the product of Monochromatic absorption coefficient and distance raised to the power of exponent. Monochromatic Transmissivity is denoted by 𝜏_λ symbol.

How to calculate Monochromatic Transmissivity using this online calculator? To use this online calculator for Monochromatic Transmissivity, enter Monochromatic Absorption Coefficient (α_λ) & Distance (x) and hit the calculate button. Here is how the Monochromatic Transmissivity calculation can be explained with given input values -> 0.693919 = exp(-(0.42*0.87)).

FAQ

What is Monochromatic Transmissivity?

The Monochromatic Transmissivity formula is defined as the product of Monochromatic absorption coefficient and distance raised to the power of exponent and is represented as 𝜏_λ = exp(-(α_λ*x)) or Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance)). Monochromatic Absorption Coefficient is defined as the proportionality constant where thickness of the gas layer and the intensity of radiation are proportional & Distance is the length across which the absorption of radiation beam is taking place.

How to calculate Monochromatic Transmissivity?

The Monochromatic Transmissivity formula is defined as the product of Monochromatic absorption coefficient and distance raised to the power of exponent is calculated using Monochromatic Transmissivity = exp(-(Monochromatic Absorption Coefficient*Distance)). To calculate Monochromatic Transmissivity, you need Monochromatic Absorption Coefficient (α_λ) & Distance (x). With our tool, you need to enter the respective value for Monochromatic Absorption Coefficient & Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Monochromatic Transmissivity?

In this formula, Monochromatic Transmissivity uses Monochromatic Absorption Coefficient & Distance. We can use 2 other way(s) to calculate the same, which is/are as follows -

Monochromatic Transmissivity = 1-Monochromatic Absorption Coefficient
Monochromatic Transmissivity = 1-Monochromatic Absorption Coefficient

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