1. SOLAR ENERGY
Our Sun is about five billion years old and accounts for 99.9% of the total mass of this solar system. Most scientists are optimistic that we’ll still have a functional sun billions of years from now.
DIAMETER: 1,390,000 km
MASS: 1.99 trillion, trillion, billion kg
SURFACE TEMPERATURE: 5,800 K
CORE TEMPERATURE: 15,600,000 K
ENERGY OUTPUT: 386 billion, billion mega watts/second
POWER LEVEL AT EARTH: 1.4 kilo watts/sq meter
DIAMETER: 1,390,000 km
MASS: 1.99 trillion, trillion, billion kg
SURFACE TEMPERATURE: 5,800 K
CORE TEMPERATURE: 15,600,000 K
ENERGY OUTPUT: 386 billion, billion mega watts/second
POWER LEVEL AT EARTH: 1.4 kilo watts/sq meter
Each second about 700,000,000 tons of hydrogen are converted to about 695,000,000 tons of helium and 5,000,000 tons of energy in the form of gamma rays. As it travels out toward the surface, the energy is continuously absorbed and re-emitted at lower and lower temperatures so that by the time it reaches the surface, it is primarily visible light.
Even though solar energy is the largest source of energy received by the Earth, its intensity at the Earth’s surface is actually very low due to the large distance between the Earth and the sun and the fact that the Earth’s atmosphere absorbs and scatters some of the radiation. Even on a clear day with the sun directly overhead, the energy that reaches the Earth’s surface is reduced about 30 percent by the atmosphere. When the sun is near the horizon and the sky is overcast, the solar energy at ground level can be negligible. It also varies from one point to another on the Earth’s surface. Nevertheless, in the 20th century, the sun’s energy has become an increasingly attractive source for small amounts of direct power to meet human needs. A number of devices for collecting solar energy and converting it into electricity have been developed, and solar energy is used in a variety of ways.
Solar energy is energy emitted by a star. Figure (1.1) shows the anatomy of a star. We saw in the preceding section that the energy emitted by a star is generated by nuclear fusion. The fusion process occurs in the core, or center, of the star. Energy released by the fusion process propagates away from the core by radiating from one atom to another in the radiation zone of the star. As the energy moves away from the core and passes through the radiation zone, it reaches the part of the star where energy continues its journey toward the surface of the star as heat associated with thermal gradients. This part of the star is called the convection zone. The surface of the star, called the photosphere, emits light in the visible part of the electromagnetic spectrum. The star is engulfed in a stellar atmosphere called the chromosphere. The chromosphere is a layer of hot gases surrounding the photosphere.
Even though solar energy is the largest source of energy received by the Earth, its intensity at the Earth’s surface is actually very low due to the large distance between the Earth and the sun and the fact that the Earth’s atmosphere absorbs and scatters some of the radiation. Even on a clear day with the sun directly overhead, the energy that reaches the Earth’s surface is reduced about 30 percent by the atmosphere. When the sun is near the horizon and the sky is overcast, the solar energy at ground level can be negligible. It also varies from one point to another on the Earth’s surface. Nevertheless, in the 20th century, the sun’s energy has become an increasingly attractive source for small amounts of direct power to meet human needs. A number of devices for collecting solar energy and converting it into electricity have been developed, and solar energy is used in a variety of ways.
Solar energy is energy emitted by a star. Figure (1.1) shows the anatomy of a star. We saw in the preceding section that the energy emitted by a star is generated by nuclear fusion. The fusion process occurs in the core, or center, of the star. Energy released by the fusion process propagates away from the core by radiating from one atom to another in the radiation zone of the star. As the energy moves away from the core and passes through the radiation zone, it reaches the part of the star where energy continues its journey toward the surface of the star as heat associated with thermal gradients. This part of the star is called the convection zone. The surface of the star, called the photosphere, emits light in the visible part of the electromagnetic spectrum. The star is engulfed in a stellar atmosphere called the chromosphere. The chromosphere is a layer of hot gases surrounding the photosphere.
The luminosity of a star is the total energy radiated per second by the star. The luminosity of the sun is approximately 3.8 × 1026 W. Radiation from the sun is comparable to the radiation emitted by a black body at 6000ºK. The amount of radiation from the sun that reaches the earth’s atmosphere is called the solar constant and is approximately equal to 1370 watts per square meter. The solar constant varies with time because the earth’s axis is inclined and the earth follows an elliptical orbit around the sun. The distance between a point on the surface of the earth and the sun varies throughout the year. To account for the time dependence, we write the solar constant as a function of time S(t).
The amount of solar radiation that reaches the surface of the earth depends on the factors. The flux of solar radiation incident on a surface placed at the edge of the earth’s atmosphere depends on the time of day and year, and the geographical location of the surface. The geographical location of the surface can be identified by its latitude θlat and longitude θlong.
where the angle θ(t, θlat, θlong) is the angle between the incident solar flux at time t and the normal to the surface at latitude θlat and longitude θlong. Some incident solar radiation is reflected by the earth’s atmosphere. The fraction of solar radiation that is reflected back into space by the earthatmosphere system is called the albedo. The albedo is approximately 0.35, which is due to clouds (0.2), atmospheric particles (0.1), and reflection by the earth’s surface (0.05).
Once in the atmosphere, solar radiation can be absorbed in the atmosphere or scattered away from the earth’s surface by atmospheric particulates such as air, water vapor, dust particles, and aerosols. Some of the scattered light eventually reaches the surface of the earth as diffused light. Solar radiation that reaches the earth’s surface from the disk of the sun is called direct solar radiation if it has experienced negligible change in its original direction of propagation.
Solar energy is freely available to all. It cannot be cut off by blockade or embargo. Nor does it involve the burning of any scarce fuels or the generation of any pollution. It cannot be exhausted for it will last as long as the sun shines.
With this sort of potential it is no wonder that people are excited by solar energy. However, there are disadvantages too. While the total amount of solar energy is great, it is spread over a vast area. To be useful, it must be collected and concentrated. This means that lots of space is needed for mirrors or collectors. Solar energy is also subject to interruption. It is not available on cloudy days or at night. To insure a dependable energy supply, the captured energy must be stored in some way or supplemented with a back-up system. In addition, solar energy is not as flexible in its application as are more conventional sources of power. A fuel tank or an electric motor can be placed almost anywhere, but to use solar energy you need plenty of room in a sunny place in which to spread solar collectors. As long as fuel is cheap, there is no particular reason to suffer these disadvantages for the sake of using solar energy. Now, that the cost of energy is rising sharply, solar energy is getting a lot more attention.
The availability of solar energy varies from place to place according to the prevailing weather conditions. In the Southwest, with its high percentage of clear days and nights, solar energy is at its best. In areas like the Pacific Northwest, or northern New York state, it is limited because of frequent clouds and overcast. By consulting an almanac or atlas, or Weather Bureau records, you can find out how much sun you can expect in your area each season.
Solar radiation is measured in langleys, a unit named after Samuel Langley Who invented instrument for measuring solar radiation. One Langley is radiation energy equivalent to one calorie falling on an area of one square centimeter. The measurements are taken on a horizontal surface at ground level. The solar radiation flux varies from zero to 1.5 langleys per minute. One langley per minute is a typical value to expect on a clear day. Since the sun’s radiation is measured on a horizontal surface, the experimenter can expect a bit more when he tills his collector toward the sun so that it is perpendicular to the sun’s rays.
where the angle θ(t, θlat, θlong) is the angle between the incident solar flux at time t and the normal to the surface at latitude θlat and longitude θlong. Some incident solar radiation is reflected by the earth’s atmosphere. The fraction of solar radiation that is reflected back into space by the earthatmosphere system is called the albedo. The albedo is approximately 0.35, which is due to clouds (0.2), atmospheric particles (0.1), and reflection by the earth’s surface (0.05).
Once in the atmosphere, solar radiation can be absorbed in the atmosphere or scattered away from the earth’s surface by atmospheric particulates such as air, water vapor, dust particles, and aerosols. Some of the scattered light eventually reaches the surface of the earth as diffused light. Solar radiation that reaches the earth’s surface from the disk of the sun is called direct solar radiation if it has experienced negligible change in its original direction of propagation.
Solar energy is freely available to all. It cannot be cut off by blockade or embargo. Nor does it involve the burning of any scarce fuels or the generation of any pollution. It cannot be exhausted for it will last as long as the sun shines.
With this sort of potential it is no wonder that people are excited by solar energy. However, there are disadvantages too. While the total amount of solar energy is great, it is spread over a vast area. To be useful, it must be collected and concentrated. This means that lots of space is needed for mirrors or collectors. Solar energy is also subject to interruption. It is not available on cloudy days or at night. To insure a dependable energy supply, the captured energy must be stored in some way or supplemented with a back-up system. In addition, solar energy is not as flexible in its application as are more conventional sources of power. A fuel tank or an electric motor can be placed almost anywhere, but to use solar energy you need plenty of room in a sunny place in which to spread solar collectors. As long as fuel is cheap, there is no particular reason to suffer these disadvantages for the sake of using solar energy. Now, that the cost of energy is rising sharply, solar energy is getting a lot more attention.
The availability of solar energy varies from place to place according to the prevailing weather conditions. In the Southwest, with its high percentage of clear days and nights, solar energy is at its best. In areas like the Pacific Northwest, or northern New York state, it is limited because of frequent clouds and overcast. By consulting an almanac or atlas, or Weather Bureau records, you can find out how much sun you can expect in your area each season.
Solar radiation is measured in langleys, a unit named after Samuel Langley Who invented instrument for measuring solar radiation. One Langley is radiation energy equivalent to one calorie falling on an area of one square centimeter. The measurements are taken on a horizontal surface at ground level. The solar radiation flux varies from zero to 1.5 langleys per minute. One langley per minute is a typical value to expect on a clear day. Since the sun’s radiation is measured on a horizontal surface, the experimenter can expect a bit more when he tills his collector toward the sun so that it is perpendicular to the sun’s rays.
Solar heat collectors
Solar heat collectors capture sunlight and transform radiant energy into heat energy. Figure (1.3) is a diagram of a solar heat collector. Sunlight enters the collector through a window made of a material like glass or plastic. The window is designed to take advantage of the observation that sunlight is electromagnetic radiation with a distribution of frequencies. The window in a solar heat collector is transparent to incident solar radiation and opaque to infrared radiation.
The heat absorber plate in the solar heat collector is a dark surface, such as a blackened copper surface, that can be heated by the absorption of solar energy. The surface of the heat absorber plate emits infrared radiation as it heats up. Sunlight enters through the window, is absorbed by the heat absorber plate, and is reradiated in the form of infrared radiation. Greenhouses work on the same principle; the walls of a greenhouse allow sunlight to enter and then trap reradiated infrared radiation. The window of the solar heat collector is not transparent to infrared radiation, so the infrared radiation is trapped in the collector.
The solar heat collector must have a means of transferring collected energy to useful energy. A heat transfer fluid such as water is circulated through the solar heat collector. and carries heat away from the solar heat collector for use elsewhere.
The sun is highest in summer, lowest in winter, and midway between during spring and fall. The designer can take advantage of this by tilting the collectors so hat it faces the sun squarely during the time of year when energy is most needed. For instance, a collector in a solar home heating system will be tilled to face the low winter sun so that the collector will work best during the coldest part of the year. The coils of a collector are nearly always blackened to make them more efficient at absorbing light and converting it to heat. Unfortunately, black is also good at radiating heat, and most of this re-radiated heat is lost. To stop this, some collectors use selective surfaces. Theses are coatings which are good at absorbing light, but poor at radiating heat. The use of selective surfaces makes a collector much more efficient. Unfortunately the making of selective surfaces is beyond the amateur at present.
The amount of energy gathered by a collector depends to some extent on the flow rate of that heat transfer fluid through it. If the rate of flow slow, the fluid has plenty of time to reach a fairly high temperature. On the other hand, the hotter the collector is allowed to get, the more heat it will lose to its surroundings. When the rate of flow is fast, the fluid does not warm up very much. However, a larger amount of fluid is warmed, and since the losses are less in this mode, the total amount of energy delivered by the collector is greater.
Solar heat collectors capture sunlight and transform radiant energy into heat energy. Figure (1.3) is a diagram of a solar heat collector. Sunlight enters the collector through a window made of a material like glass or plastic. The window is designed to take advantage of the observation that sunlight is electromagnetic radiation with a distribution of frequencies. The window in a solar heat collector is transparent to incident solar radiation and opaque to infrared radiation.
The heat absorber plate in the solar heat collector is a dark surface, such as a blackened copper surface, that can be heated by the absorption of solar energy. The surface of the heat absorber plate emits infrared radiation as it heats up. Sunlight enters through the window, is absorbed by the heat absorber plate, and is reradiated in the form of infrared radiation. Greenhouses work on the same principle; the walls of a greenhouse allow sunlight to enter and then trap reradiated infrared radiation. The window of the solar heat collector is not transparent to infrared radiation, so the infrared radiation is trapped in the collector.
The solar heat collector must have a means of transferring collected energy to useful energy. A heat transfer fluid such as water is circulated through the solar heat collector. and carries heat away from the solar heat collector for use elsewhere.
The sun is highest in summer, lowest in winter, and midway between during spring and fall. The designer can take advantage of this by tilting the collectors so hat it faces the sun squarely during the time of year when energy is most needed. For instance, a collector in a solar home heating system will be tilled to face the low winter sun so that the collector will work best during the coldest part of the year. The coils of a collector are nearly always blackened to make them more efficient at absorbing light and converting it to heat. Unfortunately, black is also good at radiating heat, and most of this re-radiated heat is lost. To stop this, some collectors use selective surfaces. Theses are coatings which are good at absorbing light, but poor at radiating heat. The use of selective surfaces makes a collector much more efficient. Unfortunately the making of selective surfaces is beyond the amateur at present.
The amount of energy gathered by a collector depends to some extent on the flow rate of that heat transfer fluid through it. If the rate of flow slow, the fluid has plenty of time to reach a fairly high temperature. On the other hand, the hotter the collector is allowed to get, the more heat it will lose to its surroundings. When the rate of flow is fast, the fluid does not warm up very much. However, a larger amount of fluid is warmed, and since the losses are less in this mode, the total amount of energy delivered by the collector is greater.
Energy Conversion Efficiency
The temperature of a solar heat collector does not increase indefinitely because the window and walls of the solar heat collector cannot prevent energy from escaping by conduction and radiation. The collector will emit thermal radiation according to the Stefan–Boltzmann law when its temperature is greater than ambient temperature. The Stefan–Boltzmann law says that the net energy ΔQrad radiated through a surface area A by an object at absolute temperature T with surroundings at absolute temperature Te during a time interval Δt is.
where σ is the Stefan–Boltzmann constant, and e is the thermal emissivity of the object at absolute temperature T. Thermal emissivity is a dimensionless quantity, and the thermal emissivity of a black body is 1. The temperature of the solar heat collector will increase until thermal equilibrium is established. The energy balance for thermal equilibrium must include energy output as well as energy loss, thus
Einput = Eoutput + Eloss
The energy conversion efficiency ηshc of the solar heat collector
The efficiency ηshc depends on the increase in temperature relative to ambient temperature, the intensity of solar radiation, and the quality of thermal insulation. An example of an expression for the efficiency ηshc for a solar heat collector with commercial insulation
where a0, b0 are empirical constants, Tamb is ambient temperature in degrees Celsius, T is the temperature in degrees Celsius of the solar heat collector at a given time, Is is incident solar intensity at a given time, and Ismax is the maximum solar intensity observed at the location of the solar heat collector.
Hayden presented an energy conversion efficiency example for a solar heat collector characterized by empirical constants a0 = 80%, b0 = −0.89/ºC and at a location with a maximum solar intensity Ismax = 950 W/m2. Efficiency ηshc is in percent for these constants, and the temperatures T, Tamb are in degrees Celsius. The negative sign in empirical constant b0 shows that an increase in the temperature of the solar heat collector T relative to ambient temperature Tamb causes a decrease in efficiency, and a decrease in incident solar intensity Is from its maximum value Ismax causes a decrease in efficiency. The incident solar intensity Is can decrease by more than 50% in cloudy (or smoggy) conditions relative to Ismax. The efficiency of converting solar energy to heat decreases because there is less solar energy impinging on the collector. An increase in solar heat collector temperature T relative to ambient temperature Tamb causes a decrease in intensity because of energy losses associated with convection and thermal radiation. The loss of energy by convection and radiation causes a decrease in energy conversion efficiency.
The temperature of a solar heat collector does not increase indefinitely because the window and walls of the solar heat collector cannot prevent energy from escaping by conduction and radiation. The collector will emit thermal radiation according to the Stefan–Boltzmann law when its temperature is greater than ambient temperature. The Stefan–Boltzmann law says that the net energy ΔQrad radiated through a surface area A by an object at absolute temperature T with surroundings at absolute temperature Te during a time interval Δt is.
where σ is the Stefan–Boltzmann constant, and e is the thermal emissivity of the object at absolute temperature T. Thermal emissivity is a dimensionless quantity, and the thermal emissivity of a black body is 1. The temperature of the solar heat collector will increase until thermal equilibrium is established. The energy balance for thermal equilibrium must include energy output as well as energy loss, thus
Einput = Eoutput + Eloss
The energy conversion efficiency ηshc of the solar heat collector
The efficiency ηshc depends on the increase in temperature relative to ambient temperature, the intensity of solar radiation, and the quality of thermal insulation. An example of an expression for the efficiency ηshc for a solar heat collector with commercial insulation
where a0, b0 are empirical constants, Tamb is ambient temperature in degrees Celsius, T is the temperature in degrees Celsius of the solar heat collector at a given time, Is is incident solar intensity at a given time, and Ismax is the maximum solar intensity observed at the location of the solar heat collector.
Hayden presented an energy conversion efficiency example for a solar heat collector characterized by empirical constants a0 = 80%, b0 = −0.89/ºC and at a location with a maximum solar intensity Ismax = 950 W/m2. Efficiency ηshc is in percent for these constants, and the temperatures T, Tamb are in degrees Celsius. The negative sign in empirical constant b0 shows that an increase in the temperature of the solar heat collector T relative to ambient temperature Tamb causes a decrease in efficiency, and a decrease in incident solar intensity Is from its maximum value Ismax causes a decrease in efficiency. The incident solar intensity Is can decrease by more than 50% in cloudy (or smoggy) conditions relative to Ismax. The efficiency of converting solar energy to heat decreases because there is less solar energy impinging on the collector. An increase in solar heat collector temperature T relative to ambient temperature Tamb causes a decrease in intensity because of energy losses associated with convection and thermal radiation. The loss of energy by convection and radiation causes a decrease in energy conversion efficiency.
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