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

The correct option is B

6 kg

Initially ice will absorb heat to raise it's temperature to $0^{\circ }$ then it's 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

loss by water $\Rightarrow m_i\times c\times \left(20\right)+m_i^{\prime }\times L=m_w{c}_w\left[20\right]$

$\Rightarrow 2\times 0.5\left(20\right)+m_i\times 80=5\times 1\times 20\Rightarrow m_i^{\prime }=1kg$

So final mass of water = initial mass of water +

Mass of ice that melts = 5 + 1 = 6 kg