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.

Answer 1

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