Question

$2\, kg$ of ice at $-20^{\circ} C$ is mixed with $5\, kg$ of water at $20^{\circ} C$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1\, kcal / kg$ per ${ }^{\circ} C$ and $0.5\, kcal / kg /{ }^{\circ} C$ while the latent heat of fusion of ice is $80\, kcal / kg$.

• A. 7 kg
• B. 6 kg
• C. 4 kg
• D. 2 kg

Answer 1

Answer: (B)

Initially ice will absorb heat to raise its temperature to $0^{\circ} C$ then its melting takes place If $m_{i}=$ Initial mass of ice, $m_{i}'=$ Mass of ice that melts and $m_{W}=$ Initial mass of water By Law of mixture Heat gained by ice $=$ Heat lost by water
$\Rightarrow m_{i} \times c \times(20)+m_{i}' \times L=m_{W} c_{W}[20]$
$\Rightarrow 2 \times 0.5(20)+m_{i}' \times 80=5 \times 1 \times 20$
$\Rightarrow m_{i}'=1\, kg$
So final mass of water = Initial mass of water + Mass of ice that melts $=5+1=6\, kg$.