How much ice is needed to cool one can of Coca-Cola from room temperature (72 ºF) to the ice point of 32 ºF?

Question

How much ice is needed to cool one can of Coca-Cola from room temperature (72 ºF) to the ice point of 32 ºF?The can contains 355 g of liquid whose specific heat is 4.20 kJ/(kg∙C°). The latent heat of fusion of water is 335 kJ/kg. The heat capacity of the 15-g can may be ignored.

4.5 g

99 g

178 g

355 g

1270 g

Answer 1

First figure the energy removed from the Coke to lower the temperature 40 F (72 --> 32), but be careful this is an asinine problem because all the other units are in SI so you need to use a delta T in C, not F. Watch other units too...

dQ = mCpdT

dQ = 0.355 * 4.2 * (22.2 - 0)

dQ = 33.1 kJ

This energy is to be absorbed by the ice, and to use the minimum amount of ice you'll want just enough to melt completely with none left over.  The energy needed to melt ice is given by the latent heat of fusion (Hsl):

dQ = Hsl * m, where m is the mass of ice. Solve for m:

m = dQ / Hsl = 33.1 / 335

m = 99g

Of course we assume a reversible (isentropic and adiabatic) process.