BB_SPECTRAL_RAD
This function computes blackbody spectral radiance at a specified wavelength using Planck’s law. It models the ideal thermal emission from a surface at absolute temperature T and is useful for radiation analysis in thermal engineering and heat-transfer calculations.
The spectral radiance is given by:
I_{\lambda}(\lambda, T) = \frac{2 h c^2}{\lambda^5\left[\exp\left(\frac{h c}{\lambda k T}\right)-1\right]}
where h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, \lambda is wavelength, and T is absolute temperature.
Excel Usage
=BB_SPECTRAL_RAD(T, wavelength)T(float, required): Temperature of the surface (K).wavelength(float, required): Wavelength of interest (m).
Returns (float): Spectral radiance in W/(m^2srm), or an error message if invalid.
Example 1: Blackbody radiance at 800 K and 4 micrometers
Inputs:
| T | wavelength |
|---|---|
| 800 | 0.000004 |
Excel formula:
=BB_SPECTRAL_RAD(800, 0.000004)Expected output:
1311690000
Example 2: Blackbody radiance at 5778 K and 500 nm
Inputs:
| T | wavelength |
|---|---|
| 5778 | 5e-7 |
Excel formula:
=BB_SPECTRAL_RAD(5778, 5e-7)Expected output:
26375700000000
Example 3: Blackbody radiance at 1000 K and 1 micrometer
Inputs:
| T | wavelength |
|---|---|
| 1000 | 0.000001 |
Excel formula:
=BB_SPECTRAL_RAD(1000, 0.000001)Expected output:
67204600
Example 4: Blackbody radiance at 300 K and 10 micrometers
Inputs:
| T | wavelength |
|---|---|
| 300 | 0.00001 |
Excel formula:
=BB_SPECTRAL_RAD(300, 0.00001)Expected output:
9924030
Python Code
Show Code
from ht.radiation import blackbody_spectral_radiance as ht_blackbody_spectral_radiance
def bb_spectral_rad(T, wavelength):
"""
Compute blackbody spectral radiance at a wavelength.
See: https://ht.readthedocs.io/en/latest/ht.radiation.html
This example function is provided as-is without any representation of accuracy.
Args:
T (float): Temperature of the surface (K).
wavelength (float): Wavelength of interest (m).
Returns:
float: Spectral radiance in W/(m^2*sr*m), or an error message if invalid.
"""
try:
T_val = float(T)
wavelength_val = float(wavelength)
if T_val <= 0:
return "Error: T must be greater than 0"
if wavelength_val <= 0:
return "Error: wavelength must be greater than 0"
return ht_blackbody_spectral_radiance(T_val, wavelength_val)
except Exception as e:
return f"Error: {str(e)}"