Remember we are expecting the “effective”
solar constant to be about 379 J s–1 m–2. The
density of water is 1 kg per liter. The amount of
water in the bottle is 200 ml, or 0.20 liter. Therefore,
the mass of the water is 0.20 kg. Now, the
specific heat capacity of water is 4,186 J kg–1K–1,
and since we have only 0.20 kg, we should get
1 degree temperature rise for every 0.20 x 4,186
joules of energy input. That is, every 837 joules
of energy input should produce 1 degree rise in
temperature.
Now we need to determine the energy input
expected from the solar radiation. The face of
the bottle is about 8 cm by 9 cm, or it has an
area of 72 cm2
. When we convert this to meters,
we get 7.2 x 10–3m2
. Therefore we may expect to
collect 379 x 7.2 x 10–3 = 2.73 Js–1. This comes out
to be about 164 J per minute. Since it will take
837 J to produce a 1-degree rise in temperature,
we will have to wait 837/164 minutes, or 5.1
minutes, for the temperature to increase by 1
degree. In order to read the temperature rise of
the thermometer reasonably accurately, we will
want it to change by 3 or 4 degrees. This means
that we should expect to wait 15 to 20 minutes
or so before recording the temperature rise