Properties Of Solids And Liquids Question 564
Question: 2 kg of ice at $ 20{}^\circ C $ is mixed with 5kg of water at $ 20{}^\circ 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 $ 1kcal/kg/{}^\circ C $ and $ 0.5kcal/kg/{}^\circ C $ while the latent heat of fusion of ice is 80 kcal/kg
Options:
A) 7kg
B) 6kg
C) 4kg
D) 2kg
Show Answer
Answer:
Correct Answer: B
Solution:
Initially ice will absorb heat to raise its temperature to $ 0{}^\circ C $ then it’s melting takes place
If $ m _{1} $ = Initial mass of ice, $ m _{2} $ ’ = Mass of ice that melts and $ m _{W} $ = Initial mass of water
By Law of mixture
Heat gained by ice = Heat lost by water
$ \Rightarrow m _{1}\times ( 20 )+m _{1}’\times L=m _{W}c _{W}[ 20 ] $
$ \Rightarrow 2\times 0.5( 20 )+m _{1}’\times 80=5\times I\times 20 $
$ \Rightarrow {{\text{m}} _{\text{1}}}’\text{ =1kg} $
So, final mass of water = Initial mass of water + Mass of
Ice that melts = 5 +1 = 6kg
