Imagine a puddle of water, 1 cm deep. Direct sun rays are used to evaporate the
ID: 1583356 • Letter: I
Question
Imagine a puddle of water, 1 cm deep. Direct sun rays are used to evaporate the water at 0°C. How long will it take to evaporate the water completely? [The latent heat of vaporisation for water is 540 cal. g-1 at 100°C and 600 cal. g-1 at 0°C. The solar constant is 1.97 cal.cm-2 .min-1 , or 1372 W .m-2. Remember that one cubic centimetre (1 cm3) of water = 1 g, so you can consider the puddle to be made up of lots of cubes of water, each 1 cm deep, and 1 cm2 on their top surfaces.
This is a very simplistic question with no further information.
Explanation / Answer
Intensity of sun light, I = 1372 W/m^2
let A is the area of the puddle.
d = 1 cm = 0.01 m
Lv = 600 cal/g
= 600*4.28/(10^-3 kg)
= 2.568*10^6 J/kg
mass of water in the puddle, m = density*volume
= 1000*A*d
= 1000*A*0.01
= 10*A
let t is the time taken to evaporate the water.
Energy oborbed by water, Q = power*time
= I*A*t (since Intensity = Power/Area)
now use, Q = m*Lv
I*A*t = 10*A*2.568*10^6
t = 10*2.568*10^6/I
= 10*2.568*10^6/1372
= 18717 s or 312 min 5.2 hours <<<<<<<<--------------Answer