I was going to make some Ramen when my neighbor came to the

I was going to make some Ramen when my neighbor came to the door just as the water was boiling in my 25cm diameter stainless steel pan sitting on the stove. I visited with my neighbor for 45 minutes, and returned to find the water level in my pan dropped by 10 cm. Calculate the rate of heat transfer to the pan.

Solution

Given,

diameter = 25 cm

radius(r) = d/2 = 25/2 = 12.5 cm = 0.125 m

h = 10 cm = 0.1 m

time (t) = 45 min = 45*60 s

Volume = pi*r^2*h = 3.14*0.125^2*0.1 = 4.906*10^-3 m^3

mass of water = 1000 kg/m^3 * 4.906*10^-3 m^3

mass rate of evaporization = ( 4.906*10^-3 m^3 * 10^3 kg/m^3) / ( 45*60 s)

= 1.817*10^-3 kg/s

latent heat of water (h_fg) = 2257.03 kJ/Kg

rate of heat = latent heat of water (h_fg) *   mass rate of evaporization

= (2257.03 kJ/Kg) * (1.817*10^-3 kg/s)

= 4.101 J

rate of heat =