A vessel with a negligible heat capacity contains $1000 g$ ice at $0 ° C$ . Into it is poured $100 g$ of water at $100 ° C$ . What would be the result at the end of experiment ?
[Take SHC of water $= 4.2 {Jg}^{- 1} {{}^{\circ}C}^{- 1}$ and SLH of ice $= 336 {Jg}^{- 1}$ ]

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Solution

Step 1: Given data
Mass of ice $= 1000 g a t 0 ° C$
Mass of water $= 100 g a t 100 ° C$
SHC of water $= c = 4.2 {Jg}^{- 1} {{}^{\circ}C}^{- 1}$
SLH of ice $= L = 336 {Jg}^{- 1}$
Step 2: The heat given out by water in cooling from $100 ° C$ to $0 ° C$
$= m c (100 - 0) = 100 m c = 100 \times 42 \times 100 = 42000 J$

Step 3: The heat absorbed by $1000 g$ ice at $0 ° C$ in changing into $0 ° C$ water,
$= m L = 1000 \times 336 = 336000 J > 42000 J$
This means that whole of the ice is not melted as heat given out by hot water is less than needed.

Step 4: Finding the result at the end of the experiment.
Let $m$ be the mass of ice that melts by heat supplied by not water.
$Q = m L 42000 = m \times 336 336 \times m = 42000 m = \frac{42000}{36} = 125 g$
Mass of the ice that does not melt = $1000 - 125 = 875 g$
Hence at the end of the experiment $875 g$ of ice does not melt and the final temp. is $0 {}^{\circ}C$ .

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A vessel with a negligible heat capacity contains 1000g ice at 0°C. Into it is poured 100g of water at 100°C. What would be the result at the end of experiment ?[Take SHC of water =4.2Jg-1C∘-1and SLH of ice =336Jg-1 ]

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