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.

Answer 1

Given:
Initial temperature of the water, T_i = 20°C
Final temperature of the water (room temperature), T_f = 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
$\Rightarrow$100 h = 315×10⁵ J
$\Rightarrow$ h = 315×10³ m = 315 km