Classical Mechanics
# Phase Transitions

Consider an aluminium cup with mass $140.0 \text{ g}$ at $60 ^\circ\text{C}$ and water with a mass of $600.0 \text{ g}$ contained in this cup at the same temperature. If the temperature of both the cup and water decreases to $57 ^\circ\text{C},$ approximately how much energy is removed from the cup-water system?

The specific heat of water and aluminuim are $4187 \text{ J/kg}\cdot\text{K}$ and $900 \text{ J/kg}\cdot\text{K},$ respectively.

If we immerse a steel ball with mass $0.8 \text{ kg}$ initially at $800 \text{ K}$ into a styrofoam box containing $35.0 \text{ kg}$ of water at $300 \text{ K},$ what is the approximate final temperature of the water at equilibrium, assuming that water was not vaporized and the water-steel ball system is thermally isolated?

The specific heat of water and steel are $4187 \text{ J/kg}\cdot\text{K}$ and $448 \text{ J/kg}\cdot\text{K},$ respectively.

Approximately how much heat must be absorbed by water of mass $m=450.0 \text{ g}$ at $0^\circ\text{C}$ to increase its temperature to $27 ^\circ\text{C}?$

The specific heat of water is $4187 \text{ J/kg}\cdot\text{K}.$