Answer to Question #245017 in Physics for emily

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 620W/m², how long does it take to increase the temperature of 1.8m³ of water from 21°C to 46°C? Take the water specific heat capacity to be 4186 J/(^oC kg). Take the density of water to be 1g/cm³ . State your answer in minutes to the nearest minute. Do not enter the units.

Answer 1

The time it will take can be found from the equilibrium of heat required to raise the temperature of water and the power supplied:

$$t=\frac Q{P}=\frac{cm\Delta \tau}{Ap},\\\space\\ t=\frac{4186·1000·1.8(46-21)}{12·620}=25319\text{ s},$$

or 7 h 2 min.