Answer to Question #107360 in Physics for Nyx

Question

A 33 g ice cube at −14◦C is dropped into a
container of water at 0◦C.
How much water freezes onto the ice? The
specific heat of ice is 0.5 cal/g ·
◦ C and its heat
of fusion of is 80 cal/g.
Answer in units of g.

Answer 1

The equation of heat balance says

$$c_{ice}m_{ice}\Delta T=\lambda m_{water}.$$

Hence, the amount of water that freezes

$$m_{water}=\frac{c_{ice}m_{ice}\Delta T}{\lambda}$$ $$=\frac{0.5\times 33\times 14}{80}=2.9\:\rm g$$