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 ${}^{\circ }Cand0.5kcal/kg{/}^{\circ }C$ 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

The correct option is B 6 kg

Initially ice will absorb heat to raise it's temperature to $0^{\circ }C$ then it's melting takes place
If m = Initial mass of ice, m' = Mass of ice that melts and $m_w$ = Initial mass of water
By Law of mixture Heat gain by ice = Heat loss by water
$\Rightarrow m\times c\times \left(20\right)+m^{\prime }\times L=m_w{C}_w\left[20\right]\Rightarrow 2\times 0.5\left(20\right)+m^{\prime }\times 80=5\times 1\times 20\Rightarrow m^{\prime }=1kg$
So final mass of water = Initial mass of water + Mass of ice that melts = 5 + 1= 6 kg.