Question

2 kg of ice at $-{20}^{o}C$ is mixed with 5 kg of water at ${20}^{o}C$ 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 $kcal/kg{/}^{o}C$ and 0.5 $kcal/kg/{}^{o}C$ 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

Intially ice will absorb heat to raise it's temperature to $0^{o}c$ then it's melting takes place

If $m_i$=initial mass of ice, $m_i^{\prime }$=Mass of ice that melts and $m_w$ = initial mass of water

By Law of mixture, Heat gained by ice = Heat lost by water $\Rightarrow m_i\times c\times \left(20\right)+m_i^{\prime }\times L=m_w{c}_w\left[20\right]$
$\Rightarrow 2\times 0.5\left(20\right)+m_i^{\prime }\times 80=5\times 1\times 20\Rightarrow m_i^{\prime }=1kg$

So final mass of water = Initial mass of water + Mass of ice that melts = 5+1=6 kg.