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.

A cup of warm water is suspended in a large pot of boiling water. Will the water in the cup ever boil?

Assume that the pot never runs out of water.

If the chocolate pope is not to be melt on a hot sunny day, what should he be made of?

For how many seconds would you need to focus the Fresnel lens on a penny in order to melt the entire coin?

**Details and assumptions:**

- A penny weighs \(2.5 \text{ g}\) and is made of \(100\)% \(\text{Cu}.\)
- The penny starts out at \(25^\circ\text{C}\) and melts at \(1085^\circ\text{C}.\)
- \(\text{Cu}\)'s heat of melting is \(176 \text{ kJ}/\text{kg}\) and its specific heat is \(0.386\text{ kJ}/\text{kg}\cdot\text{K}.\)
- The area of the lens is \(0.2 \text{ m}^2,\) the power of the sun is \(1370\text{ W/m}^2,\) and \(100\)% of the energy goes into heating the coin.

When \(\displaystyle T\) crosses \(T_c\), however, there is a qualitative shift in the allowed values of \(m^*\), and the system undergoes a phase transition.

Suppose we're working with the system at a temperature \(\displaystyle T\) below \(T_c\) such that \(T-T_c=-10\), find \(\lvert m^*\rvert\).

**Assumptions**

- The system always resides in states \(m^*\) which minimize its free energy. These are the "physical" states of the system.

×

Problem Loading...

Note Loading...

Set Loading...