Poor man's arbitrage

You've found a stockpile of 1955 United States pennies, which are now worth approximately twice as much as raw metal compared to their value as currency. A Fresnel lens can be used to concentrate incoming light onto a focal point.

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 g2.5 \text{ g} and is made of 100100% Cu.\text{Cu}.
  • The penny starts out at 25C25^\circ\text{C} and melts at 1085C.1085^\circ\text{C}.
  • Cu\text{Cu}'s heat of melting is 176 kJ/kg176 \text{ kJ}/\text{kg} and its specific heat is 0.386 kJ/kgK.0.386\text{ kJ}/\text{kg}\cdot\text{K}.
  • The area of the lens is 0.2 m2,0.2 \text{ m}^2, the power of the sun is 1370 W/m2,1370\text{ W/m}^2, and 100100% of the energy goes into heating the coin.
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