Question

On a winter day the temperature of the tap water is ${20}^{o}C$ whereas the room temperature is $5^{o}C$. 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 $10kg$ mass vertically, how high can it be lifted as the water comes to the room temperature? Take $g=10m/s^2$

• A. $215km$
• B. $315km$
• C. $115km$
• D. $105km$

Answer 1

The correct option is B $315km$

As the water comes to its room temperature, it liberates energy and this energy is utilized in increasing the potential energy of the mass.

The energy given by the water is given as:

$E_w=m_{w}s\Delta T$

and the potential energy of the mass is increased as:

$PE=mgh$

The mass of the water is $0.5\times 1000=500kg$

$s=4200\frac{kg}{k}$

The energies can be equated as follows:

$W=\left(mg\right).h=m_{w}s△T$

$10\times 10\times h=(1000\times 0.5)\times 4200\times 15$

$h=\frac{3.15\times {10}^5}{100}$

$h=315km$