You are a professional frontier re-enactor who specializes in making lead shot.

Question

You are a professional frontier re-enactor who specializes in making lead shot. To do this you put 1.8 kg of ice into 1.8 kg of water, both at 0 C, into an insulated bucket. To make the shot, you carefully drop 1 g droplets of molten lead which is exactly at the melting temperature of 327.5 C into the bucket of ice-water. The molten lead solidifies into perfect spheres and fall to the bottom of the bucket. A. How much energy is required to cool a single droplet of molten lead all the way down to 0 C? B. What is the maximum number of lead shot balls can you make without changing the ice-water temperature from 0C?

Explanation / Answer

latent heat of fusion of lead = 22.4kJ/kg latent heat of fusion of water = 334kJ/kg specific heat of lead = 0.13kJ/kg specific heat of ice = 2.108 kJ/kg-K energy required to take lead to 0C = 0.13 * 0.001 + 22.4*0.001*327.5 = 7.336 kJ for maximum number of lead shot balls, all water will cool to ice. So heat liberated will be = 1.8 * 334 = 601.2 kJ Now for 1 drop it requires 7.336kJ, so in 601.2kJ number of droplets = 601.2/7.336 = 81.95 = 81 drops approximately

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