4. (15 points) Carefully purified water can be supercooled to a temperature below $0^{\circ}$. However, if a crystal of ice is thrown into it, the water will immediately begin to freeze. What fraction of water supercooled to $-10^{\circ} \mathrm{C}$ in a thermos will freeze if a small ice chip is thrown into it? The specific heat capacity of water $c=4200$ J/(kg$\cdot$K), the latent heat of fusion of ice $\lambda=330$ kJ/kg.
4. A small ice crystal becomes a center of crystallization. The heat released during crystallization goes to heating the water. Eventually, thermal equilibrium is established at $t=0^{\circ} \mathrm{C}$.

From the heat balance equation $\quad \lambda m_{\text{ice}}=c m_{\text{water}} \Delta t$

Finally $\quad \frac{m_{\text{ice}}}{m_{\text{water}}}=\frac{c \Delta t}{\lambda}=0.13$.

(15 points)

Solutions.