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Specific Heat Capacity

On a winter d...

Question

On a winter day the temperature of the tap water is $20^{\circ} C$ whereas the room temperature is $5^{\circ} C .$ Water is stored in a tank of capacity $0.5 m^{3}$ 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 $g = 10 m s^{- 2}$

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Solution

Here $m = 0.5 m^{2} = 500 L = 500 k g$

So the heat liberated during the water changes $20^{\circ} C$ to $5^{\circ} C$

$= 500 \times 4200 \times 15$

$[Δ θ = 20 - 5 = 15]$

$= 500 \times 4200 \times 15$

$= 75 \times 420 \times 1000$

$= 31500 \times 1000$

Let the height = h

the required work

$= m g h = 10 \times 10 \times h = 100 h$

But, 100 h = 3150000

$\Rightarrow h = 315000 m = 315 k m$

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