Poor man's arbitrage
Classical Mechanics
Level
2
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.
by
Josh Silverman