energy — Radiation

Computes the total energy radiated by a body with given parameters.

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Interface

#include <codecogs/engineering/thermodynamics/radiation/energy.h>

using namespace Engineering::Thermodynamics::Radiation;

inline double energy(double T, double e = 1.0)

This module calculates the total energy radiated by a body per unit surface area in unit time.

The total radiative energy $E_0$ of a black body is given by the Stefan-Boltzmann law

$$E_0 = \int_0^{\infty} I(\lambda) {\rm d}\lambda \qquad \left[\frac{W}{m^2}\right]$$

(1)

where $I(\lambda)$ is the radiative intensity of the black body.

In practice, the following formula due to Kirchoff is used

$$E_0 = e c_0 \left(\frac{T}{100}\right)^4 \qquad \left[\frac{W}{m^2}\right]$$

(2)

where $C_0$ is the emissivity constant of the black body $\displaystyle \left(C_0 \approx 5.669 \left[\frac{W}{m^2 K^4}\right]\right)$, $e$ is the emissivity factor of the body $(0 < e \leq 1)$ and $T$ is its absolute temperature.

Example 1

The following example calculates the total radiative energy emitted by the Wolfram filament of an incandescent light bulb at 3573.16 degrees Kelvin.

#include <codecogs/engineering/thermodynamics/radiation/energy.h>
#include <stdio.h>

int main()
{
  // the temperature of the Wolfram filament
  double T = 3573.16;

  // emissivity factor of the filament
  double e = 0.39;

  // display the total radiative energy
  printf("Energy = %.5lf kW per sq. meter\n",
  Engineering::Thermodynamics::Radiation::energy(T, e)/1000.0);

  return 0;
}

Output

Energy = 3603.96794 kW per sq. meter

Parameters

the absolute temperature of the body (Kelvin)

the emissivity factor of the body (0 < e <= 1); default value 1.0

Returns

the total radiative energy emitted by the body (Watt per square meter)

A table with the emissivity factors of various materials at different temperatures can be found at the following link http://www.monarchserver.com/TableofEmissivity.pdf

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Interactive Calculator

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