Poor man's arbitrage

Classical Mechanics Level 2

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 $2.5 \text{ g}$ 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.

The answer is 5.34.

1 solution

Anish Puthuraya
Apr 1, 2014

The total heat supplied must be used to raise the temperature of the coin, as well as to melt it.

$Q_{total} = ms\Delta T + m L$

$P\cdot t = m (s\Delta T + L)$

$1370\times 0.2\times t = \frac{2.5}{1000}\left(0.386(1085-25) + 176)\right)\times 1000 J$

$t = 5.339 sec$

Q. (A+B)

md raquib - 7 years, 1 month ago

This does not matter a change in temperature is the same in Kelvin as it is in Celsius. For example going from 25 degrees Celsius to 30 degrees Celsius is a change in temperature of 5 degrees Celsius. But a change of the equivalent in Kelvin (298.15K to 303.15K) is still a change of 5K. And since when working with heat we only work with a change in temperature using degrees Celsius or Kelvin doesn't matter. The answer is 5.339 seconds. After all converting from Celsius to Kelvin only involves addition and does not change the difference between 2 temperatures only absolute values.

m vl - 1 year ago

The answer of the problem is wrong, the specific heat are in kJ/kg.K, so you need to use the TEmperature change in Kelvin, not in celsius. The result is 6.30s

Lorenzo Moulin - 5 years, 11 months ago

Temperature change in Celsius and in Kelvin are the same.

Jason Zou - 5 years, 11 months ago

Coz size of 1 Kelvin is equal to 1 Celsius change in temp will be same

Bhavik Bansal - 5 years, 11 months ago

The change is the same because if we convert from Celsius to Kelvin we add 273 to the to terms and because of the minus sign ,273 cancels -273 EX.the change between 0'C and 100'C is 100-0=100'C If we convert them to Kelvin: (100+273)-(0+273) =100 + 273 - 273 = 100 K It's the same .

Youssef Ali - 5 years, 5 months ago

Poor man's arbitrage

The answer is 5.34.

1 solution

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