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 in the vessel in kg. It is given that the specific heat of water and ice are 1 kcal/kg/°C and 0.5 kcal/kg/°C respectively and the latent heat of fusion of ice is 80 kcal/kg.

Let m kg be the mass of ice melted into water. 

Heat lost by 5 kg of water = 5 kg $\times$ 1 kcal/kg/°C $\times$ 20°C = 100 kcal. 

Heat gained = $mL+ms\Delta T$=m kg $\times$ 80 kcal/kg + 2 kg $\times$ 0.5 kcal/kg/°C $\times$ 20°C = 80 m kcal + 20 kcal.

 Now, heat gained = heat lost. 

Therefore, 80 m + 20 = 100

or m=1 kg. 

Therefore, final mass of water = 5 kg + 1 kg = 6 kg.