The neighborhood kiddie pool is 0300 m deep has a 500 m diam

The neighborhood kiddie pool is 0.300 m deep has a 5.00 m diameter. The water receives energy from sunlight at an average rate of 400 W/m^2. If the water absorbs all the solar energy and doesn\'t exchange energy with its surroundings, how many hours will it take to warm the water from 12.0^degreeC to 29.0^degreeC?

Solution

Area

A=pi*d²/4 =pi*5²/4 =19.635 m²

Volume of water

V=A*h =19.635*0.3 =5.89 m³

density of water p=1000 kg/m³

mass of water m=pV =5.89*1000

m=5890 kg

Power received by the pool from sunlight

P=IA =400*19.635

P=7854 Watts

Specific heat of water c_w=4186 J/Kg-^oC

The amount of heat energy required to rise the temperature of the water in the pool

Q=mc_w(T₂-T₁) =5890*4186*(29-12)

Q=4.2*10⁸ J

Time taken to warm the water from 12^oC to 29^oC is

t= Q/P =4.2*10⁸/7854 =53367 s

in hours

t=53367/3600 =14.82 hours