Answer to Question #245014 in Physics for Diane

Question

A water heater is operated by direct solar power. If the solar collector has an area of 12m2, and if the intensity delivered by sunlight is 620 W/m2, how long does it take to increase the temperature of 1.8m3 of water from 21 Celsius to 46 Celsius? Take the water specific heat capacity to be 4186 j/(Celsius kg). Take the density of water to be 1g/cm3. State your answer to the nearest minute.

Answer 1

The heat required to raise the temperature of water:

$$Q=Pt,\\ cm\Delta T=pAt,\\\space\\ t=\frac{cm\Delta T}{pA}=\frac{c\rho V\Delta T}{pA},\\\space\\ t=\frac{4186·1000·1.8(46-21)}{620·12}=25319\text{ s, or 7 h}.$$