A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is _______ grams. (Latent heat of fusion of lead $=2.5 \times 10^4 \mathrm{JKg}^{-1}$ and specific heat capacity of lead $=125 \mathrm{JKg}^{-1}$ $\left.\mathrm{K}^{-1}\right)$

<p>Let's determine the mass step by step:</p> <p><p>The bullet is heated from 300 K to 600 K, so the increase in temperature is:</p> <p>$\Delta T = 600\, \text{K} - 300\, \text{K} = 300\, \text{K}.$</p></p> <p><p>The heat required to raise the temperature of the bullet (using the specific heat capacity of lead) is:</p> <p>$$Q_1 = m \times c \times \Delta T = m \times 125\, \text{J/kg K} \times 300\, \text{K} = 37500\, m \, \text{J},$$</p> <p>where $ m $ is the mass in kilograms.</p></p> <p><p>After reaching 600 K, the bullet melts. The heat required for the phase change (melting) is given by:</p> <p>$$Q_2 = m \times L = m \times 2.5 \times 10^4\, \text{J/kg} = 25000\, m \, \text{J}.$$</p></p> <p><p>The total heat required for the process is:</p> <p>$Q = Q_1 + Q_2 = 37500\, m + 25000\, m = 62500\, m \, \text{J}.$</p></p> <p><p>We are given that the total heat is 625 J, so:</p> <p>$62500\, m = 625.$</p> <p>Solving for $ m $:</p> <p>$m = \frac{625}{62500} = 0.01\, \text{kg}.$</p></p> <p><p>Finally, converting the mass from kilograms to grams:</p> <p>$0.01\, \text{kg} = 0.01 \times 1000\, \text{g} = 10\, \text{g}.$</p></p> <p>Thus, the mass of the bullet is 10 grams. This corresponds to Option D.</p>