A four element electric stove has an 23cm diameter burner th

A four element electric stove has an ~23cm diameter burner that provides 2.5kW of power. A pan is filled with 4 quarts(~3.75 l) of water initially at 25 C. The water boils in 10 minutes.

Reanalyze that problem, assuming the range-to-water heat transfer efficiency is the same. Estimate the time it would take for the entire 3.75 l of water to evaporate. Report your answer in the form hr:min:sec.sec.

Solution

Specific Heat capacity of Water= 4180 J/Kg

Latent Heat Capacity of Water= 2258 KJ/Kg

Mass of water= Volume*Density= (3.75*10^-3)*1000= 3.75 Kg

Heat required by water to reach from 25 C to Boiling Temperature(100 C)=

Q1 = mC(T2-T1)= 3.75*4180*(100-75)= 1175625 J

Heat Given by coil in 10 Minutes= Q2= 2.5*1000*10*60= 1500000 J

Efficiency of Coil= (Q2/Q1) *100= 78.375%

Heat required to evaporate water from Boiling temp(100 C)=Q3= m*L= 3.75*2258*1000= 8467500J

Let the coil work for \'t\' sec.

Heat given by coil in \'t\' sec=Q4= 2500t J

Efiiciency of coil remining same:

.78375= Q3/Q4= 8467500/2500t;

t= 4321.53 Sec= 4322 seconds(Approximating)

t= 1 Hr: 12 Min: 02 Sec (time required to evaporate from boiling tempr.)

Total time required to evaporate from 25 C= 1 Hr: 22 Min: 02 Sec (Adding 10 minutes);