When the room temperature is 25^ C , an electric kettle used for preparing tea takes 2 minutes to boil 4 cups of water (where 1 cup contains 200 cc of water). Given that the cost of power consumption is Re 1.00 per unit ( 1 unit = 1000 watt-hour), determine the cost of boiling 4 cups of water if the room temperature drops to 5^ C .

Step-by-step solution

Total volume of water = 4 200 cc = 800 cc . Mass of water, m = 800 g = 0.8 kg . Specific heat capacity of water, s = 4200 J kg ⁻¹ ^ C ⁻¹ . At an initial room temperature of 25^ C , the heat required to boil the water ( 100^ C ) is: Q₁ = ms T₁ = 0.8 4200 (100 - 25) = 252000 J The kettle takes 2 minutes ( 120 s ) to boil this water. The power of the kettle is: P = Q₁ t₁ = 252000 120 = 2100 W = 2.1 kW When the room temperature drops to 5^ C , the new heat required to boil the water is: Q₂ = ms T₂ = 0.8 4200 (100 - 5)