Q 11-10-042NEETJEE MainMedium
$10$ g of ice at $0°$C is mixed with $10$ g of water at $40°$C. The final temperature and the mass of ice left are (latent heat of fusion $= 80$ cal/g)
Answer: (A) $0°$C and $5$ g
Concept. Compare the heat the water can give (cooling to $0°$C) with the heat needed to melt all the ice.
Step 1. Heat available. $10 \times 1 \times 40 = 400$ cal.
Step 2. Heat needed. $10 \times 80 = 800$ cal $> 400$ cal, so not all the ice melts and the mixture stays at $0°$C.
Step 3. Ice melted. $\dfrac{400}{80} = 5$ g, so $10 - 5 = 5$ g of ice is left.
Answer. $0°$C and $5$ g (Option A).
Solution by Sreeraj P, M.Sc Physics