Question

A hot water heater is operated by using solar power. if the solar collector has an area of 5.3 m2 , and the power delivered by sunlight is 995 w/m2 , how long will it take to increase the temperature of 1 m3 of water from 20 ◦c to 65 ◦c? the specific heat of water is 4186 j/kg · ◦ c and the density of water is 1000 kg/m3 . answer in units of h.

Answer 1

Heat absorbed by the solar collector = Area*Irradiance = 5.3*995 = 5273.5 W

Heat Q in joules absorbed in t hours = Heat used to heat water. That is,

5273.5*t = mCΔT; where mass = volume*density = 1*1000 = 1000 kg

Therefore;
5273.5t = 1000*4186*(65-20) = 188370000
t = 188370000/5273.5 = 35720.11 seconds = 35720.11/(60*60) hours ≈ 9.92 hours.

It will take approximately 9.92 hours.