Question

Concentrated solar power is a method of using the Sun's light to produce useful energy on Earth. A large system of mirrors collects light during the day and focuses it on a target which is raised to a high temperature. The energy delivered to the target is then used to generate steam which runs turbines to produce electricity. The mirrors do not have to be circular, and for some designs they focus light along a line rather than to a point .

Concentrated solar power is a practical alternative to direct solar "photovoltaic" electric because the efficiency is high and because the energy collected may be stored, for example in molten salts. However, it has a very significant environmental impact on wildlife because intense converging light may endanger birds and bats. A way to reduce that risk is to lower the temperature by collecting light in long cylindrical troughs.  

In the following: a "kilowatt" or "kW" is 1000 watts. A watt is a joule/second. A kilowatt-hour or "kWh" is a kilowatt delivered for an hour. It is a unit of energy, 1000 joules per second times the number of seconds in an hour (3600).  

1. Suppose you wanted to collect power sufficient for 10,000 homes, which on average use about 10,000 kilowatt hours a year each. Given a solar constant of 1.4 kW/m², at a site with 300 clear days a year, how much area would be needed to gather the power required? Assume the turbines have an efficiency of 40% and there are 8 hours a day of useful sunlight. Given that area, if it is covered by mirrors in a square array, what is the size of the square along one side in meters? Explain.

2. To save birds and avoid singed technicians, you design the array to use cylindrically shaped mirrors focusing light to a line on long pipes. In this way the delivered power is distributed over a larger target and the temperature of the target is kept low. What is the ideal shape of the mirror? If approximately that shape were a cylinder with a diameter of 4 meters, where would the pipe have to be above the mirror's surface?  

3. The source of the energy collected by this power station is the fusion of hydrogen within the Sun's core where it is converted to helium with a small loss of mass. How much mass does the Sun lose each year to deliver this energy to a solar power system on Earth?

Answer 1

1) No. of homes = 10,000

    Energy requirement = 10,000 kWH per year for each house

So total Energy demand is 10,000 X 10,000 KWH = 100,000,000 KWH per year

As the turbine is 40% efficient so we need 100,000,000 KWH / 0.4 =250,000,000 KWh per year    ----- (i)

AT POWER STATION

   solar constant   = 1.4 Kw/m2

   let area be A , it runs for 8 hrs a day for 300 days a year so we get

Total energy form power station = 1.4 X 8 X 300 X A KWH per year   ------ (ii)

Equating i and ii we get

Area A = 74,405 m2

Assuming this area to be a square we have SIde of the square is

2) The shape would be of half cylinder and the pipe would run through the axis perpendicular to the base which lies m above the base

3) we need 250,000,000 KWh per year that is equal to 9 X 1014 J

the fusion produces energy due to mass defect so

where    = lost mass , C = 3 X 10 8 m/s speed of light

so putting E = 9 X 1014 J and other values we get

= 0.01 kg or 10 g