Q: 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/°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

Ans: (b)

Sol: Heat released by 5 kg of water when temp. falls from 20°C to 0°C

$\large Q_1 = m s \Delta \theta$

$\large Q_1 = 5 \times 10^3 \times (20-0)$

= 10^{5} cal

When 2 kg at -20°C comes to a temperature of 0°C , heat taken

$\large Q_2 = m s \Delta \theta $

$\large Q_2 = 2 \times 500 \times 20 $

= 0.2 x 10^{5} cal

The remaining heat Q = Q_{1} – Q_{2}

Q = 0.8 x 10^{5} cal

Let it will melt m kg of ice ,

$\large m = \frac{Q}{L} = \frac{0.8 \times 10^5}{80 \times 10^3} $

m = 1 kg

So , the temperature of mixture will be 0°C , mass of water in it is

= 5 + 1 = 6 kg and mass of ice = 2 – 1 = 1 kg