Properties Of Solids And Liquids Question 108
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 [IIT-JEE (Screening) 2003]
Options:
A) 7 kg
B) 6 kg
C) 4 kg
D) 2 kg
Show Answer
Answer:
Correct Answer: B
Solution:
Initially ice will absorb heat to raise it’s temperature to 0oC then it’s melting takes place.
If mi = Initial mass of ice, mi’ = Mass of ice that melts and mW = Initial mass of water .
By Law of mixture Heat gained by ice = Heat lost by water
therefore $ m _{i}\times c\times (20)+m _{i}’\times L $ = $ m _{W}c _{W}[20] $
therefore $ 2\times 0.5(20)+m _{i}’\times 80 $ = $ 5\times 1\times 20 $
therefore $ m _{i}’ $ = 1kg .
So final mass of water = Initial mass of water + Mass of ice that melts = 5 + 1= 6 kg.
