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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.
Consider a steel H-beam with mass \(130.0 \text{ kg}\) and length \(10.0 \text{ m}.\) If it absorbs a thermal energy of \(1.8 \times 10^6 \text{J},\) what is the approximate increase in the length of the H-beam, assuming that the specific heat of steel is \(c=448 \text{ J/kg}\cdot\text{K}\) and the the coefficient of linear expansion for steel is \(\alpha=11.0 \times 10^{-6} \text{ K}^{-1}?\)
If a certain metal with mass \(0.40 \text{ kg}\) absorbs \(3.0 \text{ kJ}\) of energy by heat, the temperature of the metal rises by \(17.0 ^\circ\text{C}.\) What is the approximate specific heat of the metal?
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 \(4187 \text{ J/kg}\cdot\text{K}.\)