First slide

Change of state

Question

2 kg of ice at $- 20^{0} C$ is mixed with 5 kg of water at $20^{0} C$ in an insulating vessel having a negligilble 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 $^{0} C$ and 0.5 kcal/kg/ $^{0} C$ while the latent heat of fusion of ice is 80 kcal/kg

Moderate

A

7 kg
B

6 kg
C

4 kg
D

2 kg

Solution

Initially ice will absorb heat to raise its temperature to $0^{0} C$ then its melting takes place If $m_{i} = Initial mass of ice, {m_{i}}^{'} = Massof ice that melts$ and $m_{w} = initial mass of water$
By Law of mixture Heat gained by ice = Heat lost by water $\Rightarrow m_{i} \times c \times (20) + {m_{i}}^{'} \times 80 = 5 \times 1 \times 20 \Rightarrow {m_{i}}^{'} = 1 kg$
${⇒ 2×0.5(20) + m}_{1}^{'} \times 80 = 5 \times 1 \times 20 \Rightarrow {m_{1}}^{'} = 1 k g$
So final mass of water = Initial mass of water + Mass of ice that melts = 5+1 = 6 kg.

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