2 kg of ice at -20° 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.

Question

2 kg of ice at -20° 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. (A) 7 kg (B) 6 kg (C) 4 kg (D) 2 kg

Tardigrade Admin · Accepted Answer

Initially ice will absorb heat to raise its temperature to

0^{\circ} C

then its 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 (20) + m_{i}^{'} \times L = m_{W} c_{W} [20]

\Rightarrow 2 \times 0.5 (20) + m_{i}^{'} \times 80 = 5 \times 1 \times 20

\Rightarrow m_{i}^{'} = 1 k g

So final mass of water = Initial mass of water + Mass of ice that melts

= 5 + 1 = 6 k g

.