7. Solar Energy and Light

Most of this section’s longer entries were written by Dr. Canek Fuentes-Hernandez, my paid reader of the solar chapter (see p. 161). When I was finishing Carbon Ideologies, solar power seemed our best hope. Hence the length and detail in these entries.

1 [gram-mean] calorie per square centimeter = 1 langley = 3.685 BTUsft2

Adoption constraints—“The problem[s] with the adoption of solar energy and other renewables (i.e. wind), are first and foremost related to economic and energy policy (e.g. how do we define the cost-of-power, economic subsidies, incentives to move from a centralized to a distributed model of energy production, decommissioning existing resources, etc., not to mention politics). From a technological perspective, the grand challenge facing renewables relates not to the abundance of these resources or the conversion efficiency of the associated technologies, but to electricity storage and capacity; since the grid demands are out-of-phase with the daily cycle of solar insolation, weather conditions and seasonal variations[;] and customers expect a reliable electricity output on demand.”

Blackbody—see here.

Candle and candela—“The candela (cd) is defined as the luminous intensity . . . in the horizontal direction of a standard lamp which is made and used in accordance with U.S. Bureau of Standards specifications . . . The luminous intensity of an ordinary sperm candle . . . in the horizontal direction is about 1 candle (cd).” “Every 1-cd point source of light emits 12.57 lm” = lumens.

1 international candle = 1/60 × [brightness of a blackbody [see here] at the temperature of the freezing point of platinum = 1,769° Celsius]

Foot-candle—A lumen per square foot. A measure of visible light (used for engineering); hence not directly translatable into units of solar insolation. [The same obviously goes for lumens and luxes.]

However, 1 langley per minute = [approx.] 6,700 foot-candles

The relative brightnesses of moonlight and sunlight might respectively be 1/100 and 10,000 foot-candles.

1 langley = “1 calorie of radiation energy per square centimeter” = 1 cal-cm2 = 3.69 BTUs/ft2 = 4.184 × 104 J/m2

“Radiation of 1 langley [per minute] is a reasonable average value to take for a tilted surface under a cloudless sky.”

Over the course of an hour, 1 square foot receiving 1 langley per minute will take in 221 BTUs.

1 langley per minute = 221 BTUs per square foot per hour = 3.683 BTUs/ft2-min

Lumen—1 lumen [lm] is “that quantity of incident luminous flux” to produce 1 foot-candle on each point of a 1-square-foot surface. The efficiency of an electric light source is currently defined lumens per watt (of source divided by output).

Efficiency of Edison’s lamp, 1879: 1.5 lm/watt

Efficiency of a standard warm white 100-watt fluorescent Mazda lamp, ca. 1958: 52.0 lm/watt

Lux—A lumen per square meter.

1 lux = 0.1 foot-candles

Solar absorption—“Electromagnetic radiation interacts with matter by being either absorbed, reflected or transmitted. Generally speaking, for the purpose of energy generation, we need electromagnetic radiation to be absorbed[, and it can be only] . . . if the energy carried by the electromagnetic field is equal to the energy associated with the transition from a ground state to an excited state of the material. The discrete nature of the absorption of electromagnetic radiation, is thus akin to the process of buying a product [i]n a store. We need to have the exact amount of money (electromagnetic energy) to purchase a specific product (excited state) for the store (the body that is absorbing the energy) to take it and make the monetary transaction. Each store has a wide variety of products of different prices . . . representing the band gap of the material. If we do not have enough money to buy this product, we can only go through the store without buying anything and the store becomes ‘transparent’ to us.

“Upon absorption, the energy contained by the electromagnetic radiation field generates excess energy in the material which needs to be dissipated; nature likes thermodynamic equilibrium . . . Two distinct phenomena can be identified which are always present when electromagnetic radiation is absorbed by a material.

“[1] Electromagnetic radiation generates heat. Energy absorbed by a body is dissipated through molecular or atomic vibrations leading to the generation of heat (radiant heat); causing an increased temperature, which in turn, increases the intensity of electromagnetic power radiated until thermodynamic equilibrium is achieved. Because molecules have vibrational excited states with energies in the infrared and microwaves . . . the process of “absorbing heat” from a source of electromagnetic energy (i.e. the sun) is most efficient at these, longer, wavelengths; which is why we use microwaves to heat our food instead of visible light.

“[2] Electromagnetic radiation generates . . . more electromagnetic radiation: Photoluminescence.

“Absorbed energy is dissipated through the reemission of electromagnetic energy. This process is never lossless and the reemitted electromagnetic radiation carries less energy than the incoming one. Energy loss is converted into heat and results in an increased temperature. Since molecules have electronic excited states with energies in the visible and UV range, the process of photoluminescence is most efficient at these wavelength ranges.

“We can generally say that the first phenomenon can be optimized to provide an avenue for the conversion of solar energy to thermal energy. Despite sounding counterintuitive, the second process can be optimized to convert solar energy directly into electricity. However, optimizing these two types of energy conversions require[s] materials with very different properties.”

Solar constant—The rate at which solar energy strikes the top of our atmosphere:

2 langleys per minute = 2 cal/cm2-min = 7.37 BTUs/ft2-min

Solar efficiency—“Modern concentrated solar systems . . . have maximum theoretical efficiency values (limited by Carnot’s principle, which states that the maximum efficiency of a thermal engine operating between a low temperature reservoir and a high temperature reservoir is given by one minus the ratio of these two temperatures) of around 70% times the efficiency of the solar collection by the receiver, which can be typically high.”

Solar energy—“Solar energy impinges [on] the earth in the form of electromagnetic radiation; not heat. Electromagnetic radiation is a physical phenomenon that we identify as ‘light’ in the narrow spectral window that our eyes perceive. ‘Light’ nevertheless represents only a very small portion of the total electromagnetic spectrum emitted by the sun, or any black body radiator for that matter. Cosmic rays, X-rays, ultraviolet light, infrared light, microwaves, radio, etc. are all manifestations of electromagnetic radiation, only differentiated by the amount of energy they carry (higher energy goes with higher frequencies or shorter wavelengths).”