Questions based on phase change

Question

2 kg of ice at – 10°C is mixed with 5 kg of water at 20°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 °C and 0.5 kcal/kg/°C while the latent heat of fusion of ice is 80 kcal/kg

Moderate

Solution

Initially 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, ${m}_{i}\text{'}$ = Mass of ice that melts and ${m}_{W}$ = Initial mass of water

By Law of mixture Heat gained by ice = Heat lost by water $\Rightarrow {m}_{i}\times c\times \left(10\right)+{m}_{i}\text{'}\text{\hspace{0.17em}}\times L={m}_{W}{c}_{W}\left[20\right]$

$\Rightarrow 2\times 0.5\left(10\right)+{m}_{i}\text{'}\times 80=5\times 1\times 20\Rightarrow {m}_{i}\text{'}=\frac{9}{8}\text{\hspace{0.17em}}kg$

So final mass of water = Initial mass of water + Mass of ice that melts $=5+\frac{9}{8}=\frac{49}{8}kg$

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