ENPH257: THERMODYNAMICS
8: Manipulating solar and thermal radiation
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ELECTRICITY PRODUCTION
Solar radiation can be converted into
electricity either:
• Directly
• By promoting electrons across a bandgap in
a photovoltaic semiconductor
• Indirectly
• Standard thermodynamic heat engine*
powered by concentrated sunlight
* of which, more later...
By Milko Vuille - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=36875751
© Chris Waltham, UBC Physics & Astronomy, 2017
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PHOTOVOLTAICS
• Bandgaps are measured in eV, which neatly converts into circuit voltage, so need to express
the solar spectrum in photon eV.
• The energy of a photon 𝐸𝛾 =
ℎ𝑐
𝜆
• ℎ𝑐 in appropriate units is 1240 eV.nm
• Solar spectrum: 400 nm photon (blue end) has an energy of 3.1 eV, and a 700 nm photon
(red end) has 1.8 eV.
• The associated potentials of a few volts are right in the range of electrochemistry and smallscale electronics (one might wonder why – the reason is anthropic, or at least one of biocompatibility).
© Chris Waltham, UBC Physics & Astronomy, 2017
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PHOTOVOLTAICS
• Photovoltaics work broadly as follows:
• A solar photon of energy Eγ is absorbed by a
photocell with a bandgap energy of EB. To do this
Eγ has to be bigger than EB and the cell produces
only EB’s worth of electrical energy (red curve).
• The rest (Eγ – EB) goes to heat, which produces an
optimization problem.
• The Sun produces a range of photon energies,
and only some photons have enough to raise an
electron across the bandgap. However any energy
they have above EB is wasted.
© Chris Waltham, UBC Physics & Astronomy, 2017
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PHOTOVOLTAICS
• The blue line is the (idealized) solar spectrum on Earth.
The red line is the electrical power generated by a
photovoltaic cell of bandgap 1.1 V, which corresponds
to a maximum wavelength of 1.13 μm. At the
maximum wavelength, all the photon energy is
converted to electrical work. At half this wavelength –
double the photon energy – only half the photon
energy is used in this way. At higher energies, the
efficiency is even less. The ideal efficiency of such a
cell is 45%, the ratio of areas under the two curves.
• Of course we are ignoring all kinds of real-world
effects like reflection and ohmic resistance.
© Chris Waltham, UBC Physics & Astronomy, 2017
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REAL SOLAR SPECTRA
Spectral model of a
summer noon in
Vancouver BC, using
code by Bird and
Riordan. Spectrum of
power falling on a
surface facing the Sun
normally.
Free download of excel
spreadsheet:
http://rredc.nrel.gov/so
lar/models/spectral/
© Chris Waltham, UBC Physics & Astronomy, 2017
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SOLAR CONCENTRATORS
Because the Sun extends over a very small solid angle (i.e.
approximately parallel incoming rays) we can build large area
solar collectors that concentrate sunlight onto a much
smaller area. These are non-imaging devices, and the
maximum concentration factor is related to the inverse of the
Sun’s solid angle, and is about 40,000.
The point of large concentration factors is to achieve high
temperatures in small volumes and, for example, run external
heat engines, whose efficiency rises with temperature.
Unfortunately radiant losses also rise with temperature.
•
Rubén O. Nicolás and Julio C. Durán, "Theoretical maximum concentration factors for solar
concentrators," J. Opt. Soc. Am. A 1, 1110-1113 (1984)
© Chris Waltham, UBC Physics & Astronomy, 2017
20 MW Gemsolar plant, Fuentes de Andalucía, Sevilla
© TORRESOL ENERGY
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RECENT PROGRESS I
MIT experiment to boil water
without solar concentration,
using only common materials
© Chris Waltham, UBC Physics & Astronomy, 2017
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RECENT PROGRESS II
University of Colorado team produced
a film that has a passive cooling power
of nearly 100 W/m2 under an Arizona
Sun on a clear day.
© Chris Waltham, UBC Physics & Astronomy, 2017
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RECENT PROGRESS II
The cooling is achieved by
tuning the material to match
the radiation environment:
© Chris Waltham, UBC Physics & Astronomy, 2017
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SOLAR AND THERMAL INFRARED RADIATION
•
•
•
•
Enormous power flows
Largely untapped resource
Can manipulate by changing surfaces
Thin films can be made in large areas with cheap materials and low impact on Earth’s
resources
• My wish: a surface that
•
•
•
•
•
Has high (thermal) emissivity and low (visible) reflectance below 20 C
Has low (thermal) emissivity and high (visible) reflectance above 20 C
Switches automatically
Can survive a few years in Vancouver’s weather without maintenance
Free passive heating, free passive cooling
© Chris Waltham, UBC Physics & Astronomy, 2017