Question

Equal quantities by weight of water at +50.0˚C and of ice at -40.0˚C are mixed together. What will the final state of the system (that is, what will be the final temperature and phase; and if two phases are present, how much of each)?

Answer 1

Heat capacity of ice = 2.03 (J/g 0C)

Heat capacity of water = 4.179 (J/g 0C)

Heat of fusion of ice = 333.55 J/g

When ice and water are mixed ice will convert to water and water will convert to ice.

If 1 g of each is present in the mixture, then

Heat required for ice at - 40 C to convert to ice at 0 C = 1 g * 2.03 (J/g 0C) * [0-(-40 C)]

= 81.2 J

Heat released by water at 50 C to convert to water at 0 C = 1 g * 4.719 (J/g 0C) * [(50 C) - (0 C)]

= 208.95 J

Extra heat released by water = 208.95 - 81.9 =127.75 J

The extra heat will melt some of the ice. Amount of ice melted by 127.75 J heat

= (127.75 J) / (333.55 J/g)

= 0.383 g

= 38.3 % of ice initially used to make the mixture

So the final stage of the mixture is: Mixture of ice and water at 0^oC. 38.3% of ice initially used will melt to water at 0^oC.