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# Phase Transitions

A sparsely planted forest is likely to have small scale fires while a densely packed one has the potential to burn completely — this shift is called a phase transition.

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 \(4187 \text{ J/kg}\cdot\text{K}.\)

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