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 $0.5m^3$ 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 $g=10m{s}^{-2}$

Answer 1

Here $m=0.5m^2=500L=500kg$

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

$=500\times 4200\times 15$

$[\Delta \theta =20-5=15]$

$=500\times 4200\times 15$

$=75\times 420\times 1000$

$=31500\times 1000$

Let the height = h

the required work

$=mgh=10\times 10\times h=100h$

But, 100 h = 3150000

$\Rightarrow h=315000m=315km$