Problem about a block of ice melting (specific latent heat)

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Homework Statement

A mass of 160 g of water at 100 °C is poured into the hollow. The water has specific
heat capacity 4.20 kJ kg-1 K-1. Some of the ice melts and the final mass of water in the
hollow is 365 g.
(i) Assuming no heat gain from the atmosphere, calculate a value, in kJ kg-1, for the
specific latent heat of fusion of ice. [3]

Relevant Equations

E= mcΔt
E=ml

Energy lost by water = Energy gained by ice

Energy lost by water = 0.16 x 4200 x (100-t)
Energy gained by ice = 0.205 x L + 0.205 x (t) (where t is the temperature at thermal equilibrium). However, there does not appear to be enough info to continue.

The solution, however, considered t to be 0- whilst not explicitly mentioned in the questions is this because the water remaining in the hollow and to prevent further ice melting we can assume they must have the same temperature ?

 

[jbriggs444]

The solution, however, considered t to be 0- whilst not explicitly mentioned in the questions is this because the water remaining in the hollow and to prevent further ice melting we can assume they must have the same temperature ?

Yes. We are to assume that the experimenter waited until an equilibrium was reached. An equilibrium with water and ice coexisting would naturally be at 0 degrees C.

The experimenter would be wise to do this because, as you noted, he otherwise would lack the ability to solve for the latent heat of fusion with the information that was collected.