Question

In a water tank there is 12.0 liters of water at a temperature of 44.0 °C. Boiling water at 100.0 °C is poured into the tank until the water is at 90.0 °C. How many liters of boiling water was poured into the tank? The specific heat capacity of liquid water is 4.19 kJ/kg/°C.

Answer 1

volume of water in the tank = $12l =0.012m^3$

density of water $=1000kg/m^3$

mass of water in the tank = density $\times$ volume $=0.012\times 1000=12kg$

let the water added be $x kg$

heat lost by water at 100$^0C=$ heat gained by water up to $90^0C$

$x \times 4.19\times 1000 (100-90)=(12)\times 4.19\times 1000(90-44)$

$10x=12\times 46=552$

$x=55.2kg$

volume of hot water added =$mass/density=55.2/1000=0.0552m^3=55.2litres$