Question

$4000$ calories of heat energy is supplied to crushed ice at $0^{\circ }C$, such that it completely melts to form water at $0^{\circ }C$. If specific latent heat of fusion of ice is $80cal{g}^{-1}$, what is the mass of ice?

Answer 1

Step 1: Given data

1. The heat required to melt ice is $4000$ calories and
2. The specific latent heat of fusion of ice is $80cal{g}^{-1}$.

Step 2: Calculating the mass of ice

Let the mass of the ice be $m=xgram.$

The heat required to change $0^{\circ }C$crushed ice to $0^{\circ }C$ water is

$H=m\times L$

Where

$$\begin{gathered} H=heatrequired=4000cal, \\ latentheatL=80cal{g}^{-1} \end{gathered}$$

On substituting the above-mentioned values in the above formula, we get

$$\begin{gathered} 4000=x\times 80 \\ \Rightarrow x=\frac{4000}{80} \\ \Rightarrow x=50g \end{gathered}$$

Hence, the amount of crushed ice is $50g$.