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+### Statement
+
+$13.4.17.$ [Insert the problem statement]
+
+### Solution
+
+### Problem Statement
+
+$13.4.17.$ A vessel containing 100 g of water is placed at the focus of a spherical mirror. What should be the diameter of the mirror so that the water boils in 1 minute, assuming the mirror is directed straight at the Sun? The energy flux density from the Sun is 0.14 W/cm². Neglect any losses.
+
+### Solution
+
+To boil the water, the required amount of energy is the heat of vaporization:
+
+$$Q = L \cdot m \tag{1}$$
+
+where \(L\) is the specific heat of vaporization of water. The power needed to deliver this energy in time \(t\) is:
+
+$$P = \frac{Q}{t} = \frac{L m}{t} \tag{2}$$
+
+This power is provided by the Sun’s radiation via the mirror:
+
+$$P = \varepsilon \cdot S \tag{3}$$
+
+where \(\varepsilon\) is the energy flux density given in the problem, and \(S\) is the cross-sectional area of the spherical mirror. If the diameter of the mirror is denoted by \(D\), then \(S = \frac{\pi D^2}{4}\). Equating equations (2) and (3):
+
+$$\frac{L m}{t} = \varepsilon \cdot \frac{\pi D^2}{4}$$
+
+Solving for \(D\):
+
+$$D = \sqrt{\frac{4 L m}{\pi \varepsilon t}}$$
+
+Substituting the numerical values gives:
+\(D = 1.85 \text{ m}\)
+
+#### Answer
+
+**\(D = 1.85 \text{ m}\)**
+
+#### Answer
+
+[Insert a concise answer or boxed result]