Question

$400\text{g}$ ice at $-{20}^{\circ }C$ is mixed with $200\text{g}$ water at ${40}^{\circ }C$, then which of the following statements are correct?
Given specific heat & latent heat $S_{\text{ice}}=0.5{\text{cal/g/}}^{\circ }C,$ $S_{\text{water}}=1{\text{cal/g/}}^{\circ }C$, $L_{\text{fusion(ice)}}=80\text{cal/g}$

• A. Final temperature of the mixture is ${20}^{\circ }C$
• B. Weight of ice finally is $50$ g
• C. Weight of water finally is $250$ g
• D. Weight of ice converted into water is $350$ g

Answer 1

The correct option is C Weight of water finally is $250$ g

Heat liberated when $200\text{g}$ water at ${40}^{\circ }C$ converts into water at $0^{\circ }C$
$Q=ms\Delta T=200\times 1\times 40=8000\text{cal}$
The heat aborbed when $400\text{g}$ ice at $-{20}^{\circ }C$ converts into ice at $0^{\circ }C$ is
$Q=ms\Delta T=400\times 0.5\times 20=4000\text{cal}$
So the remaining heat will be used in melting the ice.
From this heat, mass of ice which will be melted is
$m=\frac{Q}{L}=\frac{4000}{80}=50\text{g}$
Since, whole ice is not melted, thus the final temperature will be $0^{\circ }C$
$\therefore \text{ice left}=400-50=350\text{g}$
Final weight of water = $200+50=250\text{g}$