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 put2 kg of ice into 2 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

specific heat of lead = 0.128 J / gm K

Latent heat of lead = 22.4 kJ / kg = 22.4 J/g

(A) energy = 0.128 * 327.5 * 1 + 22.4 = 41.92 J + 22.4 J = 64.32 J

(B) more ice will melt as more lead is added.

So, 2 kg ice melting results in an energy equal to: latent heat * 2 = 334 * 2 kJ = 668 kJ

No. of lead shot balls = 668 * 10^3 /64.32 = 10385 balls

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