In a solar water heater, energy from the sun is gathered by water that circulate
ID: 1478556 • Letter: I
Question
In a solar water heater, energy from the sun is gathered by water that circulates through tubes in a rooftop collector. The solar radiation enters the collector through a transparent cover and warms the water in the tubes; this water is pimped into a holding tank. Assume that the efficiency of the overall system is 28% (that is, 72% of the incident solar energy is lost from the system). what collector area is necessary to raise the temperature of 190L of water in the tank from 28 to 41 in 1.1 hours when the intensity of incident sunlight is 470 W/m^2? The specific heat of water is 4186 J/kg•K. The density of water is 1.00g/cm^3
Explanation / Answer
density d = 1g/cm^3
volume V = 190 L = 190x1000 m^3
d=m/V
m = dV = 1x190x1000 g = 190 kg
Cp = 4186 J/kg.K
Q = mCpdT =190x4186x(41-28)
Q = 10339420 J
t = 1.1 hr
Q/t = 10339420/(1.1x60x60) = 2872.06 J/s
Intesity I = 0.28x470
Intesity = Q/t.A
0.28x470 = 2872.06/A
A = 2872.06/(0.28x470)
A =21.824 m2
Energy required by the water in the tank=0.001x200x1000x4187x(40°-20°)=
16748000J, to be collected in 3600s or at a rate of 16748000/3600=4652.22222J/s. At a rate of 0.2x700 J/sm² this requires a collecting area of 4652.22222/(0.2x700)=33.23m².