2 kg of ice at is mixed with 5 kg of water at 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 & ice are 1 kcal/kg/ and 0.5 kcal/kg/ whi

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 & ice are 1 kcal/kg/ ${}^{\circ}C$ and 0.5 kcal/kg/ ${}^{\circ}C$ while the latent heat of fusion of ice is 80 kcal/kg [2003]

Smart Achievers · Accepted Answer

(2)

Heat released when 5 kg of water at $20 ° C$ falls to $0 ° C$

$temperature = m C_{w} Δ T = 5 \times 1 \times 20 = 100 kcal$

$Heat required by 2 kg ice at - 20 ° C to convert into 2 kg of$ $ice at 0 ° C$ $= m C_{ice} Δ T = 2 \times 0.5 \times 20 = 20 kcal$

$Hence remaining 100 - 20 = 80 kcal of heat will melt m kg ice$ $at 0 ° C to water at 0 ° C$

$Q = m L \Rightarrow 80 = m \times 80 \Rightarrow m = 1 kg$

$Therefore the amount of water at 0 ° C = 5 kg + 1 kg = 6 kg$

$And amount of ice at 0 ° C = 2 - 1 = 1 kg$

Solution

1 7 kg

2 6 kg

3 4 kg

4 2 kg

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