Question

Water at ${100}^{\circ }C$ is poured into a bucket containing $4Kg$ of crushed ice at $0^{\circ }C$, such that all the ice melts and the final temperature recorded is $0^{\circ }C$. Calculate the amount of hot water added to the ice. [Take specific heat capacity of water $4200JK{g}^{-1}{K}^{-1}$ and specific latent heat of ice $336000JK{g}^{-1}$.

Answer 1

Step 1: Given data

1. The quantity of crushed ice is $4Kg$
2. The specific heat capacity of water $4200JK{g}^{-1}{K}^{-1}$ and specific latent heat of ice $336000JK{g}^{-1}$.

Step 2: Calculating the amount of hot water added to ice

Now let us assume what the amount of hot water is $xKg$.

The amount of heat required to melt all the ice

$$\begin{gathered} =(massoftheice\times sp.latentheatofice) \\ =(4\times 336000)J \end{gathered}$$

Heat given out by hot water

$$\begin{gathered} =massofhotwater\times sp.heatcapacityofwater\times temperaturechange \\ =x\times 4200\times (100-0) \\ =x\times 4200\times 100Jule \end{gathered}$$

By the principle of calorimetry,
Heat given out by hot water = Heat absorbed by ice

$$\begin{gathered} (x\times 4200\times 100)=4\times 336000 \\ \Rightarrow x=\frac{(4\times 336000)}{4200\times 100} \\ \Rightarrow x=3.2Kg \end{gathered}$$

Hence, the $3.2Kg$ hot water is required to melt the ice.