4 kg of ice at `-20^(@)C` is mixed with 5 kg of water at `40^(@)C`. The water content in the equilibrium mixture is `(S_("water")=1kcal//kg-C,S_(ice)=0.5kcal//kg-c,L_(f(water))=80kcal//kg)`

Options

A. 6 kg
B. 7 kg
C. 8 kg
D. 9 kg

Answer

B

Explanation

Equilibrium temperature of mixutre is `0^(@)C`
Total heat released by water `=m_(W)s_(W)Deltatheta=5xx1xx40=200kcal`
Heat taken by ice to increase its temperature from `-20^(@)C` to `0^(@)C=4xx0.5xx20=40kcal`
`therefore` mass of ice melted `=(200-40)/(80)=(160)/(80)=2kg`
`therefore` water content in the equilibrium mixture `=5+2=7kg`