While visiting San Diego, you find an old milk pitcher at the thrift shop and su

Question

While visiting San Diego, you find an old milk pitcher at the thrift shop and suspect that it is valuable because the metal is really soft, like most noble metals. You know that silver and platinum look similar, but have way different thermal conductivities (platinum is 72 W m-1 K-1, while silver is 420 W m-1 K-1). The pitcher is about 1 mm thick and has a base with a 50 mm diameter. You fill the pitcher with water and set it on a 100 W hot plate (only $0.99) and use a thermometer (also for sale at the thrift shop) to measure the temperature at the interface between the hot plate and the pitcher to stay at 100.7 °C as the water boils. Is the pitcher more likely to be silver or platinum?

Explanation / Answer

From the Question we have the following information;

Using Fourier's Law of Heat conduction; we have q = (k*A*T)/t

So, Thermal conductivity (k) = (q*t)/(A*T)

k = ( 100 W * 10-3 m) / ( 1963.5 * 10-6 m2 * 0.7 deg C) {Converting mm into SI units}

k = 72.756 W m-1 K-1

This value is close to that of platinum. So we can confirm that the pitcher is made up of platinum.

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