The country of India recently purchased a substantial amount of standard 12.4 kg

Question

The country of India recently purchased a substantial amount of standard 12.4 kg gold bars to store in their central bank. However, after the bars were delivered and analyzed, it was found that most of the bars were tungsten with a gold plating on them. This is a common criminal trick because the density of gold and tungsten are virtually the same, so bars of gold and tungsten are the same size and weight.

Density (gold) = 19.32 g /cm3

Denstiy (tungsten) = 19.25 g/cm3

Currently, tungsten only costs about $20 per pound while gold costs over $20,000 per pound. You cannot tell them apart unless you drill into the center through the gold plating to see if you have a tungsten core.

You decide to try a different method to see if you have pure gold or gold plated tungsten bars. You take a bar and apply 100 kJ of heat to the 12.4 kg bar and measure the temperature change.

Explanation / Answer

Let us consider,

specific heat of gold= 0.129 J/gºC

specific heat tungsten= 0.134 J/gºC

Q= m x DT x C = m x 0.129 J/gºC x 62.5ºC= 100000J ----> m= 12403.1g= 12.403kg

Q= m x DT x C = m x 0.134 J/gºC x 62.5ºC= 100000J ---> m= 11940.3g= 11.94kg

If the bar is made of tungsten then the mass needed to produce a DT of 62.5ºC is 11.94kg, but if the bar is made of gold the mass needed to produce that DT is 12.4kg, which is the weight of the bar that we have, so the bar is made of gold.

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