Question

Water is boiled at 1 atm pressure in a 25-cm-internal- diameter stainless steel pan on an electric range. if it is observed that the water level in the pan drops by 10 cm in 45 min, determine the rate of heat transfer to the pan.

Answer 1

3933 watts At 100 C (boiling point of water), it's density is 0.9584 g/cm^3. The volume of water lost is pi * 12.5^2 * 10 = 4908.738521 cm^3 The mass of water boiled off is 4908.738521 * 0.9584 = 4704.534999 grams. Rounding to 4 significant figures gives me 4705 grams of water. The heat of vaporization for water is 2257 J/g. So the total energy applied is 2257 J/g * 4705 g = 10619185 J Now we need to divide that by how many seconds we've spent boiling water. That would be 45 * 60 = 2700 seconds. Finally, the rate of heat transfer in Joules per second will be the total number of joules divided by the total number of seconds. So 10619185 J / 2700 s = 3933 J/s = 3933 (kg m^2/s^2)/s = 3933 (kg m^2/s^3) = 3933 watts