Question

2 kg of ice at-20c 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



container. It is given that the specific heats of water and



ice are 1 kcal/kg per °c and 0.6 kcal/kg per °c while the



latent heat of fusion of ice is 80 kcal/kg

Answer 1

I think the latent heat of ice is 80cal/gm in CGS and in SI it is 3.36x10^5...not kg...can you check your question please...

Answer 2

Given

2 kg of "ice" is at - 20℃ is "mixed" with 5 kg of 20℃;

"Specific heat" of "water" 1 kcal/kg per ℃

Specific heat of ice are 0.6 kcal/kg per ℃

Latent heat of fusion is 80 kcal/kg

5 kg of water = 5000 g of water

Heat lost by water when its temperature drops from 20℃ to 0℃

$\Rightarrow \quad 5000\quad \times \quad 20\quad =\quad 100,000\quad cals$

Heat gained by 2000 g of ice in reaching from -20℃ to 0℃

$\Rightarrow \quad 2000\quad \times \quad 0.5\quad \times \quad 20\quad =\quad 20,000\quad cals$

Remaining amount of  heat from water melting from m gram of ice

= 100,000 - 20,000 = 80,000

$\therefore \quad m\quad \times \quad 80\quad =\quad 80,000m\quad =\quad 1000\quad g$

The final mass of water in the container = 5000 + 1000 g = 6 kg