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Section (day/time):
ME139L-Experimental Heat Transfer
PreLab for Lab #4
According to the Planck distribution, the spectral distribution of black body emission is a function of
temperature and wavelength. In lab 4, we will measure irradiance from a black body radiation source at
different surface temperatures to understand the temperature dependence of radiation.
Problem 1
Suppose the surface temperature of the radiation source used in the lab is 160°C and the surface is
assumed to be black (i.e. the emissivity is 1).
a) What is the total emissive power of light emitted from the surface?
b) In practice a real detector will only be sensitive to radiation for which the wavelength falls within
5 µm
a particular band. What is the band emissive power ( ∫ E λ, b d λ) within the wavelength interval
2 µm
from 2µm to 5µm? Hint: look at sections 12.4.1 and 12.4.4 in the textbook. You can use a
calculator or computer (Wolfram Alpha, Python (scipy.integrate), Matlab, etc.) to evaluate the
definite integral. Check your units carefully!
c) What fraction of the total emissive power (Eb) falls within the specified wavelength interval?
Problem 2
Now suppose that the temperature of the radiation source is increased to 300°C
a) What is the band emissive power with wavelengths within the interval from 2µm to 5µm?
b) Compared to your answer from Problem 1b, what is the percent increase of the band emissive
power within the specified wavelength interval?
Problem 3
If the distance between the thermopile sensor and the source is tripled and all other parameters remain
the same, by what percentage will the thermopile reading increase or decrease?