Solar Heating

You must do this lab on a clear day.  (DUH!)  You will be measuring the output of the Sun at the surface of the Earth.  This will be in units of power per unit area, or Watts per square meter (W/m2).   The apparatus will be shown to you in your lab section.   

  1. Using the apparatus, heat 50 grams of water for 5 minutes.  Measure the temperature in degrees centigrade before and after to get the temperature gain: before __________, after___________, change______________.  For best results, do this step two or three times, and average your measured change in temperature.
  1. Calculate the solar power required to do this in Watts, as follows:
  1. Convert the temperature gain to calories.  To do this, remember that when you heat one gram of water one degree centigrade, you have used one calorie of energy.  You are using 50 grams of water in this experiment so you need 50 times as much energy for every degree of temperature increase.  Water heating: _________ cal.
  2. Convert calories to Joules, the metric unit of energy (4.19 Joules equals 1 calorie): _________ J.  (Check this! Which number should be bigger, the number of Joules or the number of calories?)
  3. One Joule/second (J/s) is one Watt (W).  So divide your energy in Joules by the number of seconds of solar heating in your experiment.  Solar power collected: _________ W.
  1. Measure and calculate the area of the mirror in square meters.
  1. Diameter in cm: _________ cm.
  2. Diameter in meters: _________ m.
  3. Radius in meters: _________ m.
  4. Area of circle = πr2 : _________ m2 (your web browser should display the formula as pi times radius squared).
  1. Since you didn't collect all the solar power the Sun produces, you should express just the part you collected.  This is done by quoting power (Watts) per square meter, so that you only talk about the sunlight that was collected by the mirror.  Solar power sampled: ___________ W/m2.
  1. We now have a problem that always arises when trying to collect energy, namely losses.  The energy from the Sun has passed through the glass of the mirror twice, and once through the glass in the collector.  Each pass costs you something, because the glass isn't perfectly transparent and the mirror isn't perfectly reflective (some energy is wasted because the glass and mirror also heat up).  To estimate how much solar energy REMAINS, you should write the fraction of energy remaining for each step.  In other words, if you think the mirror reflects 20% of the light (the real answer is much greater), you would write 0.2 as the fraction remaining.
The accepted value for this the solar energy falling onto the Earth above the atmosphere is about 1350 W/m2.  Divide your measured value for the solar constant by net fraction of energy available.___________________

Compare this number to your measured value.  Please comment on this (how bad were your losses? are they just due to the glass and the mirror? is your answer reasonable? if not, try to find the mistake).

 

 

 

  1. Calculate the total energy produced by the sun.  To do this, we'll need to compare the size of your solar collector (from part 3(d) above) to the size of the region where every possible ray of sunlight can land.  Look up any necessary numbers in your astronomy textbook.  We will do this two different ways, and compare the answers.  The first way uses your measured solar constant:
  1. Imagine a giant sphere surrounding the Sun with a radius equal to the Earth’s distance from the Sun (what is this distance?).  Then the Earth's orbit traces out the "equator" on that imaginary sphere.  Calculate the surface area of this sphere, since all light the Sun produces must pass through it, using the following formula:  Surface Area of a sphere = 4πr2 = _______________ m2.
  2. Multiply this (very large) number by the Watts per square meter you measured above to get the total power the Sun produces: ____________ W.
  3. Look up the accepted energy output of the Sun and calculate your percent error: ____________ % error.
The second method uses the size and temperature of the Sun:
  1. Calculate the surface area of the Sun.  Recall the formula from the previous step, but be sure to use a different radius this time:  Surface Area of a sphere = 4πr2 = _______________ m2.
  2. The energy per unit area of a black body is given by σT4, (s should show up as a greek sigma and is the Stefan-Boltzmann constant.) ____________ W/m2.
  3. Multiply these two numbers to get the total energy output from the sun: _________________W.
  4. Compare your answers using the first and the second methods.  They should be close.

  1. Describe in a sentence or two the purpose of this experiment: