On a winter day, the tap water temperature is 20^ C while the room temperature is 5^ C . Water is stored in a tank of capacity 0.5 m ^3 for household use. If it were possible to utilize the heat liberated by the water to vertically lift a 10 kg mass, how high can it be lifted as the water reaches room temperature? Take g = 10 m s ⁻² .

Step-by-step solution

Volume of water, V = 0.5 m ^3 Mass of water, M = V = 0.5 1000 = 500 kg Heat liberated by water as it cools from 20^ C to 5^ C is Q = M s T Substituting the standard specific heat of water s = 4200 J kg ⁻¹ ^ C ⁻¹ , we get: Q = 500 4200 (20 - 5) = 3.15 10^7 J This heat is utilized to lift a mass m = 10 kg to a height h . The work done is equal to the increase in potential energy. mgh = Q 10 10 h = 3.15 10^7 100 h = 3.15 10^7 h = 3.15 10^5 m = 315 km