Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 38, Problem 44P
To determine
To find:
a) The ratio
b) The ratio
c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?
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For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2000 K, let Ic represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and IP represent the corresponding intensity per unit wavelength according to the Planck expression.What is the ratio Ic/IP for a wavelength of (a) 400 nm (at the blue end of the visible spectrum) and (b) 200 mm (in the far infrared)? (c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?
A blackbody (a hollow sphere whose inside is black) emits radiation when it is heated. The emittance (Mλ, W/m3), which is the power per unit area per wavelength, at a given temperature (T, K) and wavelength (λ, m) is given by the Planck distribution, where h is Planck's constant, c is the speed of light, and k is Boltzmann's constant.
Determine the temperature in degrees Celsius at which a blackbody will emit light of wavelength 3.57 μm with an Mλ of 5.31×1010 W/m3.
The power per unit area emitted can be determined by integrating Mλ between two wavelengths, λ1 and λ2. However, for narrow wavelength ranges (Δλ), the power emitted can be simply calculated as the product of Mλ and Δλ.
power emitted=MλΔλ
Using the conditions from the first part of the question, determine the power emitted per square meter (W/m2) between the wavelengths 3.56 μm and 3.58 μm.
A blackbody is an object with a radiation spectrum that is dependent solely on its tempera-
ture. A blackbody spectrum (or spectral radiancy curve) is described by the Planck Radiation
Law.
(a)
i. Sketch the spectral radiancy curves for blackbodies with temperatures of T = 4000 K
and T = 6000 K, respectively. Describe the main differences between the two
curves in terms of the appropriate physical laws defined as a function of tempera-
ture.
ii. What is the wavelength at peak intensity for each blackbody? State the part of
the electromagnetic spectrum to which each wavelength belongs.
(b) Use the Planck Radiation Law to determine the power radiated per unit area between
the wavelengths A 500 nanometres and λ = 503 nanometres for the T 6000 K
blackbody. What fraction of the blackbody's radiancy lies in this wavelength range?
=
Chapter 38 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Prob. 5QCh. 38 - Prob. 6QCh. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10Q
Ch. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46PCh. 38 - Prob. 47PCh. 38 - Prob. 48PCh. 38 - Prob. 49PCh. 38 - Prob. 50PCh. 38 - Prob. 51PCh. 38 - Prob. 52PCh. 38 - Prob. 53PCh. 38 - Prob. 54PCh. 38 - Prob. 55PCh. 38 - Prob. 56PCh. 38 - Prob. 57PCh. 38 - Prob. 58PCh. 38 - Prob. 59PCh. 38 - Prob. 60PCh. 38 - Prob. 61PCh. 38 - Prob. 62PCh. 38 - Prob. 63PCh. 38 - Prob. 64PCh. 38 - Prob. 65PCh. 38 - Prob. 66PCh. 38 - Prob. 67PCh. 38 - Prob. 68PCh. 38 - Prob. 69PCh. 38 - Prob. 70PCh. 38 - Prob. 71PCh. 38 - Prob. 72PCh. 38 - Prob. 73PCh. 38 - Prob. 74PCh. 38 - Prob. 75PCh. 38 - Prob. 76PCh. 38 - Prob. 77PCh. 38 - Prob. 78PCh. 38 - Prob. 79PCh. 38 - Prob. 80PCh. 38 - Prob. 81PCh. 38 - Prob. 82PCh. 38 - Prob. 83PCh. 38 - Prob. 84PCh. 38 - Prob. 85PCh. 38 - Prob. 86PCh. 38 - Prob. 87PCh. 38 - Prob. 88PCh. 38 - Prob. 89PCh. 38 - Prob. 90P
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