You are making pesto for your pasta and have a cylindrical measuring cup 10.7 cm

Question

You are making pesto for your pasta and have a cylindrical measuring cup 10.7 cm high made of ordinary glass (=2.7×105(C)1) that is filled with olive oil (=6.8×104(C)1) to a height of 1.10 mm below the top of the cup. Initially, the cup and oil are at a kitchen temperature of 22.1 C. You get a phone call and forget about the olive oil, which you inadvertently leave on the hot stove. The cup and oil heat up slowly and have a common temperature.

Part A

At what temperature will the olive oil start to spill out of the cup?

Explanation / Answer

Expansion of oil is more than that of the glass.
Area of expansion for both the glass and oil is the same.
Hence the difference in increase in heights of oil and glass for a rise of temperature

{(10.7 - 0.11) 6.8e-4 - 10.7*2.7e-5}* theta = 0.11 cm

theta = 15.94 deg Celsius

Final temperature is 22.1+ 15.94= 38.04 deg Celsius

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