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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

A

7 kg
B

6 kg
C

$\frac{49}{8} k g$
D

2 kg

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, $m_{i}'$ = Mass of ice that melts and $m_{W}$ = Initial mass of water
By Law of mixture Heat gained by ice = Heat lost by water $\Rightarrow m_{i} \times c \times (10) + m_{i}' \times L = m_{W} c_{W} [20]$
$\Rightarrow 2 \times 0.5 (10) + m_{i}' \times 80 = 5 \times 1 \times 20 \Rightarrow m_{i}' = \frac{9}{8} k g$
So final mass of water = Initial mass of water + Mass of ice that melts $= 5 + \frac{9}{8} = \frac{49}{8} k g$

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