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  4. Ice at -20° C is mixed with 50g of water at 40° C . When the temperature of the mixture reaches 0° C , it is found that 20g of ice is still unmelted. choose the closest value of amount of ice added to the water from given option (Specific heat of water =4.2J/g/° C Specific heat of Ice=2.1J/g/° C Heat of fusion of water at 0° C=334J/g

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Q. Ice at $-20^\circ C$ is mixed with $50g$ of water at $40^\circ C$ . When the temperature of the mixture reaches $0^\circ C$ , it is found that $20g$ of ice is still unmelted. choose the closest value of amount of ice added to the water from given option (Specific heat
of water $=4.2J/g/^\circ C$ Specific heat of $Ice=2.1J/g/^\circ C$
Heat of fusion of water at $0^\circ C=334J/g$

NTA AbhyasNTA Abhyas 2020

Solution:

Heat lost by water $\Delta Q=ms\Delta T=50\times 1\times 40=2000\text{ cal }$
Let mass of ice $=m$
Heat gain by ice $\Delta Q=m\times \frac{1}{2}\times 20+\left(\right.m-20\left.\right)\times 80$
$=10m+80m-1600=90m-1600$
Heat gain $=$ Heat lost
$90m-1600=2000$
$m=40gm$