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Find the thermal conductivity of the paper clip in W m-1 K-1.

Two weekends ago, I drove with some friends to visit another city, took two steps away from my car after parking it, and broke my favorite flip flops (the part that goes between your toes popped out and wouldn’t stay put). This was terrible because I was going to be walking a lot at our destination.  My friend had a spare pair of shoes, but they were really ugly, so I became desperate for some functional footwear.  I found a paper clip (with a 0.8 mm diameter), grabbed it 1.5 cm from its end and popped the car’s hood to press it against the hot engine block. I held it there until it was slightly uncomfortable to hold due to its temperature (65 oC).  At that point, I assumed the tip would be hot enough to melt the polymer comprising the flip flop (150 oC), so I could poke it through the broken part to make the whole thing stay together (see photo below).  If the heat transfer rate from the engine to the paper clip is 0.5 W

(a)   find the thermal conductivity of the paper clip in W m-1 K-1.

 

(b)   This paper clip was made of brass.  Is your answer reasonable? (Hint: look up the expected value and compare)

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