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Question
On a winter day the temperature of the tap water is 20°C whereas the room temperature is 5°C. Water is stored in a tank of capacity 0.5 m3 for household use. If it were possible to use the heat liberated by the water to lift a 10 kg mass vertically, how high can it be lifted as the water comes to the room temperature? Take g = 10 m s−2.
Solution
Given:-
Initial temperature of the water, Ti = 20°C
Final temperature of the water (room temperature), Tf = 5°C
Change in temeprature, ΔT = 20°C − 5°C = 15°C
Volume of water = 0.5 m3
Density of water, d = 1000 kg/m3
Mass of the water, M = (0.5 × 1000) kg = 500 kg
Heat liberated as the temperature of water changes from 20°C to 5°C is given by
Q = M×S×ΔT
Q = (500 × 4200 × 15) J
Q = (500 × 4200 × 15) J
Q = (75 × 420 × 1000) J
Q = 31500 × 1000 J = 315×105 J
Let the height to which the mass is lifted be h.
The energy required to lift the block = mgh = 10 × 10 × h = 100 h
Acording to the question,
Q = mgh
⇒ 100 h = 315×105 J
⇒ h = 315×103 m = 315 km
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