Calculations based on stefan-boltzmann law

Stefan-boltzmann law

The Stefan-Boltzmann law relates the heat flow rate emitted or absorbed from an object to its temperature (and surface area and darkness). It was empirically derived by the Austrian physicist Joseph Stefan in 1879 and theoretically derived by the Austrian physicist LudwigBoltzmann in 1884. It is now derived mathematically from Planck's law.

\[\Phi =\varepsilon \sigma A(T^{4}- T_{0}^{4}) \]

where

\[\Phi = \] net heat flow rate [W] emitted (+) or absorbed (−)

 (epsilon) emissivity, a dimensionless (unitless) measure of a material's effective ability to emit or absorb thermal radiation from its surface; ranges from 0 (none) to 1 (maximal)

 = (sigma) Stefan's constant, 5.670 × 10−8 W/m2K4 

A = surface area [m2] of the object emitting or absorbing thermal radiation.

T= absolute temperature [K] of the object emitting or absorbing thermal radiation

T0 = absolute temperature [K] of the environment

Calculating net heat flow rate

Formula :Φ = εσA(T4 - T04)

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Output

Net heat flow rate {{hvalue}}

Calculating emissivity

Formula :ε = Φ/(σA(T4 - T04))

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Output

Emissivity of material {{evalue}}

Calculating surface area

Formula :A = Φ/(εσ(T4 - T04))

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Output

Surface area {{avalue}}

Calculating absolute temperature of the object

Formula :T = 4√(Φ/(εA)+T04)

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Output

Absolute temperature of the object {{tovalue}}

Calculating absolute temperature of the object

Formula :T0 = 4√(T4-Φ/(εA))

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Output

Absolute temperature of environment {{tevalue}}
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