Question

5 kg ice at - 40ºC is mixed with 4.5 kg water at 40ºC . Then final amount of water in the mixture will be : [Specific heat of ice = 0.5 cal/gm ºC, Specific heat of water = 1 cal/gm ºC, Latent heat of fusion of ice = 80 cal/gm ]

(A) 5.5 kg

(B) 7 kg

(C) 3.5 kg

(D)  none  of these

Answer 1

Correct option  (A) 5.5 kg

Explanation:

Heat released by 4.5 kg of water when its temperature falls from 40ºC to 0ºC is,

Q₁ = msΔθ = (4.5) (1) (40 - 0) = 180 Kcal

when 5 kg ice at -40ºC comes to a temperature of 0ºC, it takes an energy

Q₂ = msΔθ  = (5) (0.5) (40) = 100 Kcal 

The remaining heat

Q = Q₁ - Q₂ = 80 Kcal will melt mass m of the ice, where

 m = 80/80 = 1 kg

So, the temperature of the mixture will be 0ºC, mass of water in it is 4.5 + 1 = 5.5 kg and mass of ice is 5 - 1 = 4 kg.