An immersion heater rated at 1000 W , 220 V is utilized to heat 0.01 m ^3 of water. Assuming that the power is supplied at 220 V and 60 % of the supplied power goes into heating the water, determine how long it will take to raise the temperature of the water from 15^ C to 40^ C .

Step-by-step solution

Mass of water m = V = 0.01 1000 = 10 kg Heat required to raise the temperature of water is given by Q = ms T Using the specific heat capacity of water s = 4200 J kg ⁻¹ ^ C ⁻¹ : Q = 10 4200 (40 - 15) = 1050000 J Effective power utilized for heating P_ eff = 60 % of 1000 W = 600 W Time taken t = Q P_ eff = 1050000 600 = 1750 s Converting to minutes, t = 1750 60 29.16 minutes 29 minutes