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 1.4 kg of ice into 1.4 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.

How much energy is required to cool a single droplet of molten lead all the way down to 0 C? (in Joules)

What is the maximum number of lead shot balls can you make without changing the ice-water temperature from 0C?

Explanation / Answer

PART A.     Look in text to find the specific heat capacity of Lead (Pb) to be

c = 128 J/kg-degC.  

Heat Energy Lost by hot Pb = m c (delta T) = (0.001 kg) ( 128 J/kg-deg C) (327.5 C - 0 C) = 41.92 Joules for 1 ball of Pb.

PART B.    Heat Energy Gained by ice (to melt it) = Heat Energy Lost by hot Pb

            (mass of ice melted) (heat of fusion for ice) =    (41.92 J) (n lead balls)

           ( 1.4 kg ice ) ( 3.33 x 10^5 J / kg) =   (41.92 J) n

                solve for n to get    n = 11,121.18   so round to 11,121 balls of Pb can be made.  

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