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
$\large Q_1 = m s \Delta \theta$
$\large Q_1 = 5 \times 10^3 \times (20-0)$
= 105 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 105 cal
The remaining heat Q = Q1 – Q2
Q = 0.8 x 105 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