Answer to Question #175214 in Physics for Ivy kome

Question

A 100gram ice block at 20°C is dumped into thermally insulated container of water at 0°C. How much water is frozen if the specific heat capacity is 2302 J/Kg.°C and latent heat of fusion is 3.35×10^5J/Kg.

Answer 1

If the temperature of the ice block is -20°C, and the isolated container has comparably infinite mass of water, then the final temperature of the solution will be 0°C. The heat required to increase the temperature of the ice block to 0°C is

$$Q=c_im_i(0-t)=2302·0.1(0-(-20))=4604\text{ J}.$$

The water at 0░ that surrounds this piece of ice will lose its energy to increase the ice temperature, this becoming ice as well:

$$m_w\lambda=Q,\\\space\\ m_w=\frac Q\lambda=4604/335000=0.014\text{ kg},$$

or 14 g.