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 pumped into a holding tank. Assume that the efficiency of the overall system is 26.0% (that is, 74% of the incident solar energy is lost from the system). What collector area (in square meters) is necessary to raise the temperature of 110 L of water in the tank from 21°C to 42°C in 1.4 h when the intensity of incident sunlight is 530 W/m2? The specific heat of water is 4186 J/kg·K. The density of water is 1.00 g/cm3.
Explanation / Answer
The intensity of sun light falling on the earth = I' Let area of the plate = A Power received by the plate, P = I'A Efficiency of the over all system = 26 % The power given to the tank is given by P = 26% * I' A = 0.26 I'A...............(1) m= mass of 110 L of water S =specific heat of water = 4186 J/kg·K T = temparature difference = 21 deg C The energy needed to raise the temp of water from 21 to42 C is Q = mST = 9669660 J power in put needed P ' = Q / 1.0 * 60*60 sec P' = 2686.2 W ------(2) From the equations (1) and (2) we have 0.26 I'A = 2686.2 By solving the above equation we can find out the value of A for the known value of I m= mass of 110 L of water S =specific heat of water = 4186 J/kg·K T = temparature difference = 21 deg C The energy needed to raise the temp of water from 21 to42 C is Q = mST = 9669660 J The energy needed to raise the temp of water from 21 to42 C is Q = mST = 9669660 J power in put needed P ' = Q / 1.0 * 60*60 sec P' = 2686.2 W ------(2) From the equations (1) and (2) we have 0.26 I'A = 2686.2 By solving the above equation we can find out the value of A for the known value of I